notebooks/5.1 Modelling.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modelling\n",
    "\n",
    "<img src=\"figures/data-science-model.png\" width=\"500px\" heigth=\"500px\">\n",
    "\n",
    "*What is modelling?*\n",
    "\n",
    "A statistical model is a mathematical model (i.e., a description of a system or process expressed in mathematical terms), typically specified as a relationship between input variables (or independent variables) and an output (dependent) variable. Given a model or a family of models, data are used to find good configurations of it via fitting (i.e., ending with a configuration such that the output variable is predicted well from the input variables).\n",
    "\n",
    "*Why modelling?*\n",
    "\n",
    "Statistical models are used for:\n",
    "* Prediction: based on past data, we fit a model, which we use to predict on future data. \n",
    "* Inspection (or information): we use some data to fit a model and inspect it, in order to understand how different variables interact and contribute to the prediction of the output.\n",
    "\n",
    "Note that predictive or data-driven modelling (the realm of statistics and machine learning), which attempts to summarize or describe the data, is not the only way to model. Theory-driven modelling can be used instead, by formalizing a certain understanding of a system into theory taking mathematical form, such as we do in physics.\n",
    "\n",
    "For more see:\n",
    "* https://hdsr.mitpress.mit.edu/pub/9qsbf3hz\n",
    "* http://www2.math.uu.se/~thulin/mm/breiman.pdf\n",
    "\n",
    "Our working definition: *\"The goal of a model is to provide a simple low-dimensional summary of a dataset. Ideally, the model will capture true “signals” (i.e. patterns generated by the phenomenon of interest), and ignore “noise” (i.e. random variation that you’re not interested in).\"*  https://r4ds.had.co.nz/model-intro.html\n",
    "\n",
    "Topics:\n",
    "1. Linear regression (the model)\n",
    "2. Feature selection\n",
    "3. Fitting\n",
    "4. Evaluation\n",
    "5. Logistic regression (classification)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imports\n",
    "\n",
    "import os, codecs\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the dataset\n",
    "Let us import the Venetian apprenticeship contracts dataset in memory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "root_folder = \"../data/apprenticeship_venice/\"\n",
    "df_contracts = pd.read_csv(codecs.open(os.path.join(root_folder,\"professions_data.csv\"), encoding=\"utf8\"), sep=\";\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take another look to the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>page_title</th>\n",
       "      <th>register</th>\n",
       "      <th>annual_salary</th>\n",
       "      <th>a_profession</th>\n",
       "      <th>profession_code_strict</th>\n",
       "      <th>profession_code_gen</th>\n",
       "      <th>profession_cat</th>\n",
       "      <th>corporation</th>\n",
       "      <th>keep_profession_a</th>\n",
       "      <th>complete_profession_a</th>\n",
       "      <th>...</th>\n",
       "      <th>personal_care_master</th>\n",
       "      <th>clothes_master</th>\n",
       "      <th>generic_expenses_master</th>\n",
       "      <th>salary_in_kind_master</th>\n",
       "      <th>pledge_goods_master</th>\n",
       "      <th>pledge_money_master</th>\n",
       "      <th>salary_master</th>\n",
       "      <th>female_guarantor</th>\n",
       "      <th>period_cat</th>\n",
       "      <th>incremental_salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Carlo Della sosta (Orese) 1592-08-03</td>\n",
       "      <td>asv, giustizia vecchia, accordi dei garzoni, 1...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>orese</td>\n",
       "      <td>orese</td>\n",
       "      <td>orefice</td>\n",
       "      <td>orefice</td>\n",
       "      <td>Oresi</td>\n",
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       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Antonio quondam Andrea (squerariol) 1583-01-09</td>\n",
       "      <td>asv, giustizia vecchia, accordi dei garzoni, 1...</td>\n",
       "      <td>12.5</td>\n",
       "      <td>squerariol</td>\n",
       "      <td>squerariol</td>\n",
       "      <td>lavori allo squero</td>\n",
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       "      <td>Squerarioli</td>\n",
       "      <td>1</td>\n",
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       "      <th>2</th>\n",
       "      <td>Cristofollo di Zuane (batioro in carta) 1591-0...</td>\n",
       "      <td>asv, giustizia vecchia, accordi dei garzoni, 1...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>batioro</td>\n",
       "      <td>batioro</td>\n",
       "      <td>battioro</td>\n",
       "      <td>fabbricatore di foglie/fili/cordelle d'oro o a...</td>\n",
       "      <td>Battioro</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Illeggibile (marzer) 1584-06-21</td>\n",
       "      <td>asv, giustizia vecchia, accordi dei garzoni, 1...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>marzer</td>\n",
       "      <td>marzer</td>\n",
       "      <td>marzer</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
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       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Domenico Morebetti (spechier) 1664-09-13</td>\n",
       "      <td>asv, giustizia vecchia, accordi dei garzoni, 1...</td>\n",
       "      <td>7.0</td>\n",
       "      <td>marzer</td>\n",
       "      <td>marzer</td>\n",
       "      <td>marzer</td>\n",
       "      <td>merciaio</td>\n",
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       "  </tbody>\n",
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       "<p>5 rows × 47 columns</p>\n",
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      "text/plain": [
       "                                          page_title  \\\n",
       "0               Carlo Della sosta (Orese) 1592-08-03   \n",
       "1     Antonio quondam Andrea (squerariol) 1583-01-09   \n",
       "2  Cristofollo di Zuane (batioro in carta) 1591-0...   \n",
       "3                    Illeggibile (marzer) 1584-06-21   \n",
       "4           Domenico Morebetti (spechier) 1664-09-13   \n",
       "\n",
       "                                            register  annual_salary  \\\n",
       "0  asv, giustizia vecchia, accordi dei garzoni, 1...            NaN   \n",
       "1  asv, giustizia vecchia, accordi dei garzoni, 1...           12.5   \n",
       "2  asv, giustizia vecchia, accordi dei garzoni, 1...            NaN   \n",
       "3  asv, giustizia vecchia, accordi dei garzoni, 1...            NaN   \n",
       "4  asv, giustizia vecchia, accordi dei garzoni, 1...            7.0   \n",
       "\n",
       "  a_profession profession_code_strict profession_code_gen  \\\n",
       "0        orese                  orese             orefice   \n",
       "1   squerariol             squerariol  lavori allo squero   \n",
       "2      batioro                batioro            battioro   \n",
       "3       marzer                 marzer              marzer   \n",
       "4       marzer                 marzer              marzer   \n",
       "\n",
       "                                      profession_cat  corporation  \\\n",
       "0                                            orefice        Oresi   \n",
       "1                                 lavori allo squero  Squerarioli   \n",
       "2  fabbricatore di foglie/fili/cordelle d'oro o a...     Battioro   \n",
       "3                                           merciaio      Merzeri   \n",
       "4                                           merciaio      Merzeri   \n",
       "\n",
       "   keep_profession_a  complete_profession_a  ...  personal_care_master  \\\n",
       "0                  1                      1  ...                     1   \n",
       "1                  1                      1  ...                     0   \n",
       "2                  1                      1  ...                     0   \n",
       "3                  1                      1  ...                     0   \n",
       "4                  1                      1  ...                     0   \n",
       "\n",
       "   clothes_master  generic_expenses_master  salary_in_kind_master  \\\n",
       "0               1                        1                      0   \n",
       "1               0                        1                      0   \n",
       "2               0                        0                      0   \n",
       "3               0                        0                      0   \n",
       "4               0                        1                      0   \n",
       "\n",
       "   pledge_goods_master  pledge_money_master salary_master female_guarantor  \\\n",
       "0                    0                    0             0                0   \n",
       "1                    0                    0             1                0   \n",
       "2                    0                    0             0                0   \n",
       "3                    0                    0             0                0   \n",
       "4                    0                    0             1                0   \n",
       "\n",
       "  period_cat incremental_salary  \n",
       "0        NaN                  0  \n",
       "1        1.0                  0  \n",
       "2        NaN                  0  \n",
       "3        NaN                  0  \n",
       "4        1.0                  0  \n",
       "\n",
       "[5 rows x 47 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_contracts.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['page_title', 'register', 'annual_salary', 'a_profession',\n",
       "       'profession_code_strict', 'profession_code_gen', 'profession_cat',\n",
       "       'corporation', 'keep_profession_a', 'complete_profession_a',\n",
       "       'enrolmentY', 'enrolmentM', 'startY', 'startM', 'length', 'has_fled',\n",
       "       'm_profession', 'm_profession_code_strict', 'm_profession_code_gen',\n",
       "       'm_profession_cat', 'm_corporation', 'keep_profession_m',\n",
       "       'complete_profession_m', 'm_gender', 'm_name', 'm_surname',\n",
       "       'm_patronimic', 'm_atelier', 'm_coords', 'a_name', 'a_age', 'a_gender',\n",
       "       'a_geo_origins', 'a_geo_origins_std', 'a_coords', 'a_quondam',\n",
       "       'accommodation_master', 'personal_care_master', 'clothes_master',\n",
       "       'generic_expenses_master', 'salary_in_kind_master',\n",
       "       'pledge_goods_master', 'pledge_money_master', 'salary_master',\n",
       "       'female_guarantor', 'period_cat', 'incremental_salary'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_contracts.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Every row represents an apprenticeship contract. Contracts were registered both at the guild's and at a public office. This is a sample of contracts from a much larger set of records.\n",
    "\n",
    "Some of the variables we will work with are:\n",
    "* `annual_salary`: the annual salary paid to the apprencice, if any (in Venetian ducats).\n",
    "* `a_profession` to `corporation`: increasingly generic classifications for the apprentice's stated profession.\n",
    "* `startY` and `enrolmentY`: contract start and registration year respectively.\n",
    "* `length`: of the contract, in years.\n",
    "* `m_gender` and `a_gender`: of master and apprentice respectively.\n",
    "* `a_age`: age of the apprentice at entry, in years.\n",
    "* `female_guarantor`: if at least one of the contract's guarantors was female, boolean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear regression\n",
    "\n",
    "* **Regression**: predict real/continuous values given inputs (e.g., a salary of 2.15 ducats a year).\n",
    "* **Classification**: predict categorical values given inputs (e.g., there is a female guarantor in the contract or not).\n",
    "\n",
    "--> *Whiteboard*\n",
    "\n",
    "Model:\n",
    "\n",
    "$y = \\beta_0 + \\sum_{j=1}^{d}\\beta_j x_j + \\epsilon$\n",
    "\n",
    "Closed-form solution:\n",
    "\n",
    "$\\hat{\\beta} = \\Big(X^TX\\Big)^{-1}X^Ty$\n",
    "\n",
    "$\\hat{y} = x\\hat{\\beta}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's start with a toy example\n",
    "\n",
    "mean = [0, 0] # means (centers of mass)\n",
    "cov = [[5, 0], [120, 100]]  # covariance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "x, y = np.random.multivariate_normal(mean, cov, 1000, check_valid='ignore').T\n",
    "plt.plot(x, y, 'x')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.95878741],\n",
       "       [0.95878741, 1.        ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's fit a linear model to the data at hand\n",
    "\n",
    "beta = 1/(np.dot(x.T,x)) * np.dot(x.T,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7979584185067211"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta # in this 2d example this is the slope of the line!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_point = 35\n",
    "y_hat = beta * new_point\n",
    "plt.plot(x, y, 'x')\n",
    "plt.plot(new_point, y_hat, 'o', c='red')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_points = np.arange(-40,40,0.5)\n",
    "predictions = beta * new_points\n",
    "plt.plot(x, y, 'x')\n",
    "plt.plot(new_points, predictions, '.', c='red')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-40. , -39.5, -39. , -38.5, -38. , -37.5, -37. , -36.5, -36. ,\n",
       "       -35.5, -35. , -34.5, -34. , -33.5, -33. , -32.5, -32. , -31.5,\n",
       "       -31. , -30.5, -30. , -29.5, -29. , -28.5, -28. , -27.5, -27. ,\n",
       "       -26.5, -26. , -25.5, -25. , -24.5, -24. , -23.5, -23. , -22.5,\n",
       "       -22. , -21.5, -21. , -20.5, -20. , -19.5, -19. , -18.5, -18. ,\n",
       "       -17.5, -17. , -16.5, -16. , -15.5, -15. , -14.5, -14. , -13.5,\n",
       "       -13. , -12.5, -12. , -11.5, -11. , -10.5, -10. ,  -9.5,  -9. ,\n",
       "        -8.5,  -8. ,  -7.5,  -7. ,  -6.5,  -6. ,  -5.5,  -5. ,  -4.5,\n",
       "        -4. ,  -3.5,  -3. ,  -2.5,  -2. ,  -1.5,  -1. ,  -0.5,   0. ,\n",
       "         0.5,   1. ,   1.5,   2. ,   2.5,   3. ,   3.5,   4. ,   4.5,\n",
       "         5. ,   5.5,   6. ,   6.5,   7. ,   7.5,   8. ,   8.5,   9. ,\n",
       "         9.5,  10. ,  10.5,  11. ,  11.5,  12. ,  12.5,  13. ,  13.5,\n",
       "        14. ,  14.5,  15. ,  15.5,  16. ,  16.5,  17. ,  17.5,  18. ,\n",
       "        18.5,  19. ,  19.5,  20. ,  20.5,  21. ,  21.5,  22. ,  22.5,\n",
       "        23. ,  23.5,  24. ,  24.5,  25. ,  25.5,  26. ,  26.5,  27. ,\n",
       "        27.5,  28. ,  28.5,  29. ,  29.5,  30. ,  30.5,  31. ,  31.5,\n",
       "        32. ,  32.5,  33. ,  33.5,  34. ,  34.5,  35. ,  35.5,  36. ,\n",
       "        36.5,  37. ,  37.5,  38. ,  38.5,  39. ,  39.5])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's add an outlier!\n",
    "\n",
    "x[0] = 200\n",
    "plt.plot(x, y, 'x')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's fit a linear model to the data again\n",
    "\n",
    "beta = 1/(np.dot(x.T,x)) * np.dot(x.T,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_points = np.arange(-40,40,0.5)\n",
    "predictions = beta * new_points\n",
    "plt.plot(x, y, 'x')\n",
    "plt.plot(new_points, predictions, '.', c='red')\n",
    "plt.axis('equal')\n",
    "plt.xlim((-40,40))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# An example with the intercept\n",
    "\n",
    "mean = [0, 15] # means (centers of mass)\n",
    "cov = [[5, 0], [120, 100]]  # covariance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = np.random.multivariate_normal(mean, cov, 1000, check_valid='ignore').T\n",
    "plt.plot(x, y, 'x')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's fit a linear model to the data at hand\n",
    "\n",
    "beta = 1/(np.dot(x.T,x)) * np.dot(x.T,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8132595665874635"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_points = np.arange(-40,40,0.5)\n",
    "predictions = beta * new_points\n",
    "plt.plot(x, y, 'x')\n",
    "plt.plot(new_points, predictions, '.', c='red')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This does not work any longer, as the default intercept is at 0,0. We need to fit for the intercept as well as for the slope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's use a trick and add a new column to x, all to 1: this will allow us to fit for the intercept as well\n",
    "\n",
    "X = np.matrix([np.ones(x.shape[0]),x]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 2)\n",
      "[[  1.          20.73998802]\n",
      " [  1.           4.06088503]\n",
      " [  1.          -4.93940172]\n",
      " [  1.           0.71438291]\n",
      " [  1.          -3.79911562]\n",
      " [  1.           9.65086242]\n",
      " [  1.           3.62750382]\n",
      " [  1.           0.23270681]\n",
      " [  1.         -17.56021405]\n",
      " [  1.          -0.51597697]]\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(X[:10,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This is the same, but we need a little bit more machinery to deal with matrices\n",
    "\n",
    "betas = np.dot(np.linalg.inv(np.dot(X.T,X)),np.dot(X.T,y).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[15.09564833],\n",
       "        [ 0.80305349]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "betas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_points = np.arange(-40,40,0.5)\n",
    "predictions = betas[1,0] * new_points\n",
    "plt.plot(x, y, 'x')\n",
    "plt.plot(new_points, betas[0,0] + predictions, '.', c='red')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Consider the following dataset (for questions)\n",
    "from sklearn.datasets import make_regression # a simpler way to create regression data\n",
    "x, y = make_regression(n_samples=1000, n_features=1, noise=0.2)\n",
    "y = np.power(y,2)\n",
    "plt.plot(x, y, 'x')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.matrix([np.ones(x.shape[0]),x.ravel()]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.        , -0.61068271],\n",
       "        [ 1.        , -0.86442169],\n",
       "        [ 1.        ,  1.17852436],\n",
       "        ...,\n",
       "        [ 1.        , -0.86025065],\n",
       "        [ 1.        ,  0.52616311],\n",
       "        [ 1.        , -0.14044507]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "betas = np.dot(np.linalg.inv(np.dot(X.T,X)),np.dot(X.T,y).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[3632.90092199],\n",
       "        [-504.60161171]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "betas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_points = np.arange(-4,4,0.05)\n",
    "predictions = betas[1,0] * new_points\n",
    "plt.plot(x, y, 'x')\n",
    "plt.plot(new_points, betas[0,0] + predictions, '.', c='red')\n",
    "plt.xlim((-4,4))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Questions\n",
    "\n",
    "* What is the problem of applying linear regression to this dataset?\n",
    "* Try that out.\n",
    "* Can you think of a solution, still using linear regression?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature selection\n",
    "\n",
    "Let us focus on our regression task: predicting the salary of an apprentice given some other features of the contract. We need to select and inspect the variables to use, forming up our domain-specific model. The choice of the features, eventually their filtering and transformations, should be informed by our working hypothesis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9653\n",
      "7258\n"
     ]
    }
   ],
   "source": [
    "print(df_contracts.shape[0])\n",
    "\n",
    "# select a few independent variables and drop NA\n",
    "df_dataset = df_contracts[[\"annual_salary\",\"length\",\"a_age\",\"female_guarantor\",\"salary_master\",\"incremental_salary\"]].dropna()\n",
    "# only pick contracts with a salary paid by the master to the apprentice\n",
    "df_dataset = df_dataset[df_dataset.salary_master == 1]\n",
    "print(df_dataset.shape[0])\n",
    "df_dataset = df_dataset.drop(\"salary_master\",axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x1a1f8c1c18>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x540 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# watch for correlations, but be wary of very high correlations: they might signal data leackage on the dependent variable!\n",
    "\n",
    "sns.pairplot(df_dataset[[\"annual_salary\",\"length\",\"a_age\"]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting\n",
    "\n",
    "Usually we do not use the closed-form solution to fit a model. We instead rely on existing packages which offer approximate and robust methods to fit a model. There is quite much more to even linear regression than what we were able to touch upon, thus it is often a good idea, once the basics are clear, to turn to a more robust implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Add intercept\n",
    "\n",
    "y = df_dataset[[\"annual_salary\"]]\n",
    "X = df_dataset.drop(\"annual_salary\",axis=1)\n",
    "X = sm.add_constant(X, prepend=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7258, 1)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7258, 5)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>length</th>\n",
       "      <th>a_age</th>\n",
       "      <th>female_guarantor</th>\n",
       "      <th>incremental_salary</th>\n",
       "      <th>const</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0</td>\n",
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       "      <td>1.0</td>\n",
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       "      <td>1.0</td>\n",
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       "      <td>0</td>\n",
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       "      <td>6.0</td>\n",
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       "      <th>9</th>\n",
       "      <td>5.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <th>14</th>\n",
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       "      <td>0</td>\n",
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       "      <th>15</th>\n",
       "      <td>5.0</td>\n",
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       "      <td>1.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>3.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>6.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>5.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>5.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>5.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>3.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>7.0</td>\n",
       "      <td>10.0</td>\n",
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       "      <th>35</th>\n",
       "      <td>3.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>7.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>5.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <th>38</th>\n",
       "      <td>5.0</td>\n",
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       "      <td>0</td>\n",
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       "      <th>39</th>\n",
       "      <td>3.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>5.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>5.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>5.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>6.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>5.0</td>\n",
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       "    <tr>\n",
       "      <th>9619</th>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9620</th>\n",
       "      <td>7.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9621</th>\n",
       "      <td>2.5</td>\n",
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       "      <td>0</td>\n",
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       "      <th>9622</th>\n",
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       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9623</th>\n",
       "      <td>4.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9625</th>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9627</th>\n",
       "      <td>3.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9628</th>\n",
       "      <td>5.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9629</th>\n",
       "      <td>6.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9630</th>\n",
       "      <td>4.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9631</th>\n",
       "      <td>5.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9632</th>\n",
       "      <td>8.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9633</th>\n",
       "      <td>6.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9634</th>\n",
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       "      <td>12.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9635</th>\n",
       "      <td>6.5</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>9636</th>\n",
       "      <td>6.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9637</th>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9638</th>\n",
       "      <td>6.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>9639</th>\n",
       "      <td>6.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9641</th>\n",
       "      <td>4.5</td>\n",
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       "      <td>0</td>\n",
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       "      <td>6.0</td>\n",
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       "      <td>0</td>\n",
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       "      <th>9643</th>\n",
       "      <td>6.0</td>\n",
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       "      <td>0</td>\n",
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       "      <td>4.0</td>\n",
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       "      <th>9645</th>\n",
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       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9647</th>\n",
       "      <td>6.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9648</th>\n",
       "      <td>8.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9649</th>\n",
       "      <td>7.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9650</th>\n",
       "      <td>6.5</td>\n",
       "      <td>14.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9651</th>\n",
       "      <td>4.0</td>\n",
       "      <td>14.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9652</th>\n",
       "      <td>5.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7258 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      length  a_age  female_guarantor  incremental_salary  const\n",
       "1        2.0   20.0                 0                   0    1.0\n",
       "4        1.0   20.0                 0                   0    1.0\n",
       "5        6.0   16.0                 0                   0    1.0\n",
       "6        8.0    8.0                 0                   0    1.0\n",
       "9        5.0   14.0                 0                   0    1.0\n",
       "10       5.0   14.0                 0                   0    1.0\n",
       "11       6.0   11.0                 0                   0    1.0\n",
       "12       5.0   14.0                 0                   0    1.0\n",
       "14       5.0   16.0                 0                   0    1.0\n",
       "15       5.0   13.0                 0                   0    1.0\n",
       "17       5.0   17.0                 0                   0    1.0\n",
       "19       5.0   16.0                 1                   0    1.0\n",
       "20       3.0   18.0                 0                   0    1.0\n",
       "21       5.0   16.0                 0                   0    1.0\n",
       "23       6.0   11.0                 0                   0    1.0\n",
       "24       5.0   15.0                 0                   0    1.0\n",
       "28       5.0   16.0                 0                   0    1.0\n",
       "30       5.0   13.0                 0                   0    1.0\n",
       "32       3.0   18.0                 0                   0    1.0\n",
       "34       7.0   10.0                 0                   0    1.0\n",
       "35       3.0   16.0                 0                   0    1.0\n",
       "36       7.0   14.0                 0                   0    1.0\n",
       "37       5.0   11.0                 0                   0    1.0\n",
       "38       5.0   18.0                 0                   0    1.0\n",
       "39       3.0   14.0                 0                   0    1.0\n",
       "40       5.0   13.0                 0                   0    1.0\n",
       "41       5.0   14.0                 0                   0    1.0\n",
       "42       5.0   14.0                 0                   0    1.0\n",
       "43       6.0   12.0                 0                   0    1.0\n",
       "44       5.0   12.0                 0                   0    1.0\n",
       "...      ...    ...               ...                 ...    ...\n",
       "9619     5.0   12.0                 0                   0    1.0\n",
       "9620     7.0   14.0                 0                   0    1.0\n",
       "9621     2.5   15.0                 1                   0    1.0\n",
       "9622     4.0   14.0                 0                   0    1.0\n",
       "9623     4.0   14.0                 0                   0    1.0\n",
       "9625     5.0   12.0                 0                   0    1.0\n",
       "9627     3.0   12.0                 0                   0    1.0\n",
       "9628     5.0   15.0                 0                   0    1.0\n",
       "9629     6.0   14.0                 1                   0    1.0\n",
       "9630     4.0   16.0                 0                   0    1.0\n",
       "9631     5.0   17.0                 0                   0    1.0\n",
       "9632     8.0   15.0                 0                   0    1.0\n",
       "9633     6.0   14.0                 0                   0    1.0\n",
       "9634     7.0   12.0                 0                   0    1.0\n",
       "9635     6.5   12.0                 0                   0    1.0\n",
       "9636     6.0   16.0                 0                   0    1.0\n",
       "9637     5.0   12.0                 0                   0    1.0\n",
       "9638     6.0   14.0                 0                   0    1.0\n",
       "9639     6.0   14.0                 0                   0    1.0\n",
       "9641     4.5   15.0                 0                   0    1.0\n",
       "9642     6.0   14.0                 0                   0    1.0\n",
       "9643     6.0   14.0                 0                   0    1.0\n",
       "9644     4.0   14.0                 0                   0    1.0\n",
       "9645     7.0   13.0                 0                   0    1.0\n",
       "9647     6.0   12.0                 0                   0    1.0\n",
       "9648     8.0   14.0                 0                   0    1.0\n",
       "9649     7.0   13.0                 1                   0    1.0\n",
       "9650     6.5   14.0                 0                   0    1.0\n",
       "9651     4.0   14.0                 0                   0    1.0\n",
       "9652     5.0   15.0                 0                   0    1.0\n",
       "\n",
       "[7258 rows x 5 columns]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fit model\n",
    "\n",
    "mod = sm.OLS(y, X)\n",
    "res = mod.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:          annual_salary   R-squared:                       0.196\n",
      "Model:                            OLS   Adj. R-squared:                  0.196\n",
      "Method:                 Least Squares   F-statistic:                     443.0\n",
      "Date:                Fri, 26 Jul 2019   Prob (F-statistic):               0.00\n",
      "Time:                        10:10:22   Log-Likelihood:                -21368.\n",
      "No. Observations:                7258   AIC:                         4.275e+04\n",
      "Df Residuals:                    7253   BIC:                         4.278e+04\n",
      "Df Model:                           4                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "======================================================================================\n",
      "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------\n",
      "length                -1.3712      0.042    -32.455      0.000      -1.454      -1.288\n",
      "a_age                  0.1811      0.021      8.799      0.000       0.141       0.221\n",
      "female_guarantor      -0.0824      0.236     -0.349      0.727      -0.545       0.380\n",
      "incremental_salary     4.1287      0.352     11.719      0.000       3.438       4.819\n",
      "const                  9.4411      0.438     21.561      0.000       8.583      10.299\n",
      "==============================================================================\n",
      "Omnibus:                     9202.819   Durbin-Watson:                   1.911\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1890698.258\n",
      "Skew:                           6.914   Prob(JB):                         0.00\n",
      "Kurtosis:                      80.851   Cond. No.                         127.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic regression\n",
    "\n",
    "* **Regression**: predict real/continuous values given inputs (e.g., a salary of 2.15 ducats a year).\n",
    "* **Classification**: predict categorical values given inputs (e.g., there is a female guarantor in the contract or not).\n",
    "\n",
    "--> *Whiteboard*\n",
    "\n",
    "Model:\n",
    "\n",
    "$\\hat{y} = \\frac{1}{1 + e^{-\\big(\\beta_0 + \\sum_{j=1}^{d}\\beta_j x_j + \\epsilon \\big)}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# shape of a sigmoid function\n",
    "import math\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + math.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c208f1198>]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.linspace(-10,10,1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c22aac1d0>]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([sigmoid(x) for x in np.linspace(-10,10,1000)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's start again with a toy example\n",
    "\n",
    "from sklearn.datasets import make_classification # a simpler way to create classification data\n",
    "X, y = make_classification(n_samples=1000, n_features=2, n_redundant=0, n_informative=2,\n",
    "                           random_state=0, n_clusters_per_class=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 2)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1c20a988d0>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DypTXZnD3Gzdz0c3dy3XfCY4vwlATDMeurdoxw9wTjJPBvRQoBlTACKmjEEqkBvQSWfAwOH4EXEgMUPgKMu0lFOsFIcfiXQ2ef8BQB4ytwzpmWTwRpCfkdQCUGoiUBxHWi4/qVo8VR71RKoSwCCGWCCFWCiHWCiGejIdhFQmTxcQ9b96C2WYKfADMVhOZ1fTZdKzs3ryX716fEXDooIdwls78i3cenMjB3TmBIicpdYc67r4PWbNgPRI9jn7IJiOqIfTX5/PqEgWHM2vi73jDhHDysvNZOnMl2btyMJrCP+NLVgk+rw+Xw82b93xAUZ495vtOkCBWhFARGRMQ6a+AtS/YbkRU+gYlWvMJ91y/Q3cAGuAGnJD/IFI7NNOW0oHMGYA8eAOy4Clk7q3Ig5cjtfzQMb2bgTBOXSQjUkdVWIcO8Zmpu4BuUsoiIYQR+EMI8aOUclEcxq4w9LyhK7Ub12DK6zPI3pVDu4tb0XtwD5JSI3cTWjZrJROf+po9m/dxRot6nNGijj87IRin3cXi6csCYY/S+Dw+5n+7BEDPrFEEZzSvyzUjr2DV3LXM/PBXPE4PqkFFqArD370jrIbMrk17w47vsrvZtuZfzu56Jr4YQzwGo8ry2avo0u/cmI5PED+k5x/wrgW1FhhbVcjl/9EihAKW8xGW2LKzpGMqYWOjQgX3QrDoq0pZ+DJ4VhPYRJaAdxOy4ElIG4Ms/hac3wFGUDIAMyEbztIDhkZHdmPHiaN26lJf6xf5vzX6/x3/lJrDKMgp5NvXZrBk+nIyq6XTd1gfWnZrdlRjNmpbn5ET743p2N+/XsCLg8YFdNJzflrBil9WoRpCW9sZjCpJqTZy94aZMZRC+nudWpMtdL3qXLpedS4X3dydhdOWYrGa6dq/A1VqZYU9N6tGZJ2XPVv3Y02y0H/EZXz5wvdlF0wJvcdqguOHlG5k3hBwLYSSaka1BmRORCinpoaP9O0F316kUhWck/XZuGJD2K4Hy6WlHmjRAg6lHnqOKYRmBXnAORPpPQC+VXqqIgAWdDemoM/+/a9ZeiAMFVtaIy4xdSGECiwD6gPjpJSLwxwzGBgMULv2sa1qK8gp5PYWD1Bw4FBDib9+XcttLwzgsrsvOqbXBj1u99awj0J6j3rdPjRf6PNONagMeLQfLw4aF9OG6Jr565FSIoSgfst61G9Ztq5HlVqVEEIP6xxO7l49v/36R/txWu3KfPHCFHL35VOnSU02Lt+CJ8wMv3XPs8u8ZoL4Ie0TdIeO89CUybsVmfcwIvOdE2la3JGaHZk3VJ9lY0SPrSuAT6/9yd8I7mWItKcAENbLka6fSznkEjQwl1pNRsxz94J3FcGzfSdgBlNn8KzQs1xsAxBJN8fnJo8hcXHqUkof0EIIkQ5MEUI0lVKuOeyYCcAE0PPU43HdSHz72gzyDxQE6Y+7il28O+JTLrjpfKxJx7bkuLigmLwD4bNiDCYDRpMhsJnp8/gY/t4dNGnfMObaEJPFFHbZvXX1dn7++DccRU46Xt6O1hc0R1H0WUy9ZnUwWUyhomMWY+ChIITggoHnccHA8wLvT3zqa74YMwWhKCiqQPNq9B7ck78XbuTsrmcGxi8Pbqeb78f9xJxP52EwGeh9Ww8uuOk8VDV0FZPAT/GXhKbWecH9B1IrRiinTlNxWTDK79Dd/n8QXCXrAMcUZNJgfUPY1AEsfcEx2X+cAZCI9FcRwormnA1F4wkbI0eAUgW0feEsQZg7IzLfjeftHXPimv0ipcwTQvwGXAisKePwY8aSCA0lVIPC1lXbOfPcYxsTsyRZMJoMAW2Y0lSuWYkJq/7HX7+swevx0uL8pthSrPz+9UIsNnNQdko4TBYjvW46L+T1H96eydv3f4LX7UXzacz5dB6te57NY5MfQFEUzmhel4ZtzmD9kk2BDBfhD6P0HhzaDq+EGx67il6Dzmfx9GVMHT+TPVv2MXX8TKa9/TNZNSvxv9+eLFMlsjQ+n4/7z3+Crau2Bx4w29bsYOnPKxn95fCYx/nPISOFxCThndXJidSK/FIHZWR6CYM+gzbU1BtBpz2GtF0D7nkgbGDpBZjQsvvq2S5hsYAwgaU3FE8KvaYwwkkY2opH9ktl/wwdIYQV6AGEKkgdRzKrpYd93efxkZoVPi0qnqgGlcvuvhCzLVhbxWwzM2BUX0xmI+0uakmHS9tiS7ECcFqdLDSt7AVMk3MacNvYG4JeKzhYyNvDP8btcAfCN067i2WzV7N4+iHNjGenP0yP67tgshgRiqBppya8+sczZFbNiHrNKrWyOLDzILs37cVV7MZV7MJR5GT35r3875bxMf1MSlg8bTnb1+4IWjG4ivWN4s0rt5VrrP8Ulm6EnYMZTkcosT9UKzyyiJjdkhK8fySMDRFJtyBs1yKUTGTB0/qmcviTIWkwovIsPaQiwq0SlcAm68lEPLRfqgG/CiFWAX8Cs6SU0+Iw7hHTd1gfzLbgaknVoFK3aS1qNqh2XGwY9My19BncE7PVhMVmxpZi5aan+tPzxq5hj2/Utj7VTq8SdiO1NKvnrWf8fR/gdnnYvm4nU16foWushznPWeRk7uSFge+tyVaGv3sH0+yf8pP7C17+/amY9dR/+uDXkOwZn8fHsp9Xhu2RGom/fluDoyi0Qk9qMqEaGQWRfL9/1mj1v2LSS+fTxpxIs+KPUgXKLLtXQKSBKXKls5Q+cE7n0CbnYYgkPbSiZCDUKoj08SDS9di5sIFyGiLzY/R56slFPLJfVgEt42BL3GjZrRm3jhnAeyM/RTUo+Dw+6jatxVPfjzhuNqgGlTtevombnrmWguwCMqqmk7s3j/cf+ZQdG3bTrFNjLry5W6CcXwjB2FmP8cINb7Dil9X4vOE/jJpPY/anc1n9x3r2/5sd2PkMl64oFBFW20UIUe5UOK8r/BJfSiLaGo5K1TMxWYwh9qpGlcyq4VdYCUColSHrJ6RjCniWg3o6wnb1UVVNHguk9ILzJ6Rzup7TbeuPMMWuVCqEgkx5EvLv45D4RQn+vTBDHUT6+DI0zX1hzi9tqBvUqoeua+4IVRaAZ60e2jE0qdCa6dE4pQW9HHYnW1ZuJ61y6nGboUfi74UbGHHB03g9PrxuL2abiaS0JMYvfYFK1YLDH4umL+OZ/i+HZM+UF7PNxEu/PFEuPZrfv1rAp899S+7eXM7q0JhBz15LnSY1efHmccyZNA+fN3ifoEGreoxfOjbm8XP25jKwwZCgAiyA1EopfL7zHUyJVMmTFim9yJybwbMSPZNEoJfT34mSfEfs47h+Q+YOITj9UAXDWYj0l2PWhI8cT1fA3AMl482YbaooxCLodXI+imLEmmThrA6NTrhDl1Iy9qZxOO2uQFWnq9hN/oECPnrsi5Dj213UkqS0I8tmMFtNWJLNmCxGrh/dLyaHPnfyQm5qdC8XqFfz7LWvsHXVdvL2F7Dg+z8Zcs7D7Ny4m1ufH0BG1TQsSfrM32Q1kZRm44EP7i6XfZlVM3hm2sNkVk3HmmzBbDNT/YyqvPTrEwmHHgNSepDHWdgqZlxzDksNlPrXRW8ifQdiHkbaPyA0n9wH3g36xubhx2vFSNd8pHtFkBSuSHvaL7h1WEDCfAEi/aWY7TnZSGi/lMHK3/WqTbfDHSS+VR7yswvYtz30Q+3z+lj0Q+iKRVEUnvxuBEPaP1yu69hSrVx294XUbFidVj3Pjqmx9O9fL+TFQW+GXRVIKXEVu5n41Nc8POk+Plj3Gr98Oo91i/+hdpMadL26Iwd3HWTnP3vK9eBs3vUsPt/5DtvX7kA1GqjVqPopWRkZT6RWiCx4HJwzAQ1paIRIexZhPOtEmxZAOmdFEMAygHsxWPsEH+/dome6CFV3tCVFPZEeAMIAWk5Q2EQr/h4KHvNvdEoQyZDxLsLYGGE8E7J+RBZ/Dp71YGwEtutQSp1/xPfq3QEyFwwNT3hXpsNJOPUofPjYF3zz8jTcDhdS6uJbrXuezePfPFguJxSp8xCAxWamKM+OEATJ5TZuW582vVqwYvaqmMv3NZ/GdaP6YrGFxtEj8f4jn0YN82g+jb8XbAT0lU/vwT3pPbgnU9+ayS1nDg3Zsygrk6YERVGo16xO1GNKHqget5du13aife9WUR+oHreHL8d+z/R3ZuFyuDn3kjbc/Nx1IeGtkxGZe4se7y1JX/T+jcwZAFk/IeLgpOKCSCO4ArPkdSVEolYrGg9Fb6HHvoXebi9lJErSADB3huJ/CZuqaagf+FJ6/oGC0QQVZEk7MucmqDIPIYwItSoiZVi87hDpO4jMu9sfezcCGjJ5JErSNXG7xtFySsfUj4a92/Zzy5lDQzb0LEkWnvj2AVr3bF6u8Ub1eY5ls1YF5a4bzUbSK6eSuy8PKSE5I4naTWrQ/brO9LyxK44iJ49c/Bwbl26OOrbRbEBRFEaEaZBRFr2M/cusYlWNKtYkC52ubMctzw9g+9qdjOrzfJCcgGpQOKNFPcYtiU82xrsjJ/H9mz8FHqiWJDPte7dm1OdDIz5QH7v8BZbPWhVIl1QNKmmVU/lg3atRNXoqOtLzNzLn2jAVkyZIugUljk7raJCedciD/QkpkhJpiCrzEf7QifT8gzx4JWEbeVSeBajI7Ev0tnEBx26F1FEotqsDR2sFz/rzyw+rBxHJeuGRv6GG3jFJi8uMWjt4lf/hWnoT1orIfBdhKp9i65Hwn4+pHw3LZ61CKOHEt5wsmPpnucd78MO7qdOkJpZkC9YUC0azXlWavSsHr8eHz+sj/0ABq+eu461hH3Fvh1FYksyMWzKGRu3qhx2zcu0s+j90GTc8fjUfrH8t4NCL8uys/G0tOzfuLtOuaJowJfg8Pory7MyaOJch7R/h6/9NDdGH8Xk1tq/dwY4Nu2L4aYTy6xfzGdhwCBdZruXGBvfw7SvTcBW7ArIGJaJnkdIet/+9I8ih6zb5sOcX8/NHvx6RTRUG33Z0CdrDcetx5gqCMDaB1FGAWQ+DiCQQGYjMDwIOHUAWf0aoQweQ4JyNUCsjsqZB0kAwNAZTV0TGhCCHDuihmHD9WKUELR/pO4iWewdyXwvkvpZoB/sjvdEnSNGQ3u3g2UBoVo3Dvw9QMUiEXyJgTbEGSd2WoBpUktPK3+0kvXIab694kfVLNrFv2352b9nH5899GyKHC+ByuNm5cQ8/f/Qbl9zZi2Hv3M59HR/F7XTrol5C72b00Id30+L8piyfs5px935AfnYhliQzq+f+jdFsxOv2cnrzujw9dQRpEYquBj1zDa/e8W6Ik1ZVJSTs4/P4OLDrIAd2ZocdSzWq5B8ooFaj8jVk+PmT33j9rncDYaA9m8OVbOtFSgt/WMrZXc4MeW/Tim1hf1+uYhdrF2zkint7l8umCoWhUQRtbwsYwzc9D4eUEnzb9HQ+Q4O4puxJ6QDXIoRaDVn5V4RnJQgrmNohxGFuxjU3wiiH7lGoWYiUhyDloYjXFObzkc456NowQRdAOmZBwVP+Yia/4/f8hcy+Emm9TL9/66XlK9zSDupx/XDBDV/4z+yJIDFTj8A5l7QO+7pqVCMWEJWFEIIm7RtwXv+OuIrdIWl9pXEVu5j37WKklPz6xXx8Xh+KqiAUgcVm5tEvh9Hi/KZ8OfY7HrvsBRZ8/ydr569n2c8rcTs92POLcTncbFy2maevfjnidXpc35Uh424JzNhTMpO58JZu9Hvg0rBKjD6PL2Jeus/j44wWdcv3QwE+ePizmNI3VYMaMSuoar0qEaVBd2/eQ87e3HLbVVEQhtPB3IlAnjagF+BYEdF0xkshvZuR2Rcisy9D5vRHHuiEdMVHHVtzzELua4/Muw+Zew8c6AnCgjB3CHXoANqeSFbqHZtKvpM+pOt3pH0i0v1naPMXSy998zOoQMi/unb/BDKf4Jm8PxvH8QUUvog80A3pKUfxu6ExyDArA0xgPjKfcCz4T8zU/164IdAkou2FLcnbX0BxoYO2F7bgjOZ1w55jTbLwzA8P89hlLwQ+TF6Pj6FvD6Zmw+pHbVPD1qdjTbaEra4EXZcltVIyC6cu5fs3fwya0bscbt59aBJnntuQT574KmzhUQk+j4+/F20ke3dOxGyYXgPPp1ajGjxy8bP4vD5+/2qBrqludXoAACAASURBVMxYjs1gs83Mzc9dizVZ/wOTUrJ+ySZy9uTSqF39iNf2erzk+FUiy0IxqHS/rjP2guJAeKx1z7OxJls589yGVKtXhR3rd+E9THNny8p/ubP1CN5f+wrJ6RWvp2QsiPTXkEXjwfGl3qvT1BmR8hBCKXsTWEo3Mud6f7hC6r5NFiPzboesmUe10Sp9eyF/KIdvasrcwXoxjwhuXh79QaIGbJG+A/o+gnZQb2UnVDA0hIyPAuJlQhghcyI4vteLnXzZ+kqkLN0YQN9cdSLzH0Rk/RDTvQrFhkwZBoWvcCht0wRKOiJpYExjHA9Oeaf+8RNf8fVLU3E73Egp+emDX/UZrxBMevprug/ozNC3bw+7+XZ2lzP5au97/PXLGjwuDy26NY3bhts5fVpzWt3K7Nq4J6SpNIDJauaSO3vx6TPfhMzopSbZt/0AcycvwmAyRHXqAAaDSlGuPaJjdbs8jLr4Oex5kfoxRkZRBQ1an8HNz1xLqx66HG/27hxG9HyK/TsOoigCj9tLh0vbklElDY/bQ5erOtCyW1OEEKgGldSsFPLDqFoKIbCm6LPTEjXLjUs38+KgcQFZBM2nMeqLYZzTpzUvznmcZ699lRVzggtOfF4f9jw7M96bw9UPXFrue6wICGFCpAyFlKHlP9k119+0+bCZrvQhHd8iku86Yruk41vCC4p5kPu7AA6kejoi9RGk608o/oTwlZ4KWK8O/B3K/EfAt/vQsRLw/I0seh2ROjJwlhAmsF2FsF2Flt2P2Bx6KbxbkFpOzJr0StJNSEN9PYauZYO5KyJpUEwP1+PFKe3U92zZx1djvwtxeqXbs/3y2R90vLw97S4Kr3RQIr4VD3xeH9MmzGLGhNl43F46XdmOFXNWs37xpqDjVKPKjU9cTfOuZ/HOA5+EHUsourOWMYiAqQaVmg31PHKfz8dP7//CD2/NxOVw0/XqDmg+LeKKoSw0n+SCgecFHDrAU/1eYufGPUFZNb9/tQAhBFJK5nw6jy79zuWBD+5CCMENj/XjvRGf4iwV1zfbTNz+v4FkVc/E5/XRsnsz7PnFDGp8X6DlXwnP9H+ZT7e/RVpWKpfe1YsNSzZRXBicKeJyuFn525qT1qkfFVp2hLCBG1wL0Jw/glYA5vMRyXfrkgSlkNIN0g4i3f87dIFrnp6T7oqWNOD/Hfi2IHPvokxFSbW6/3oucM8n1Pm79UYXpZy6frwTMMARZbf4CL8JHRlh7oQwdzqCax0fTmmn/udPf5UZQnDaXfz8yW9xc9zReLr/yyyduTKwKTn5fz+E3ShVFEH3AZ0B6NLvXLb/vTPEkTmLXEx5YwYpWSk4i10RnbtqUBj84g0YjPqveuzAccz/bknAhs+fnxJTY45oTHjwE87q0IgzmtflwM6DbPprW9gxS8JYTruLuZMXcuHN3WjWuQmX3nUhQgg+efJrCrILMFlNeN1ext/3IZlV07l33K0kpdqYMWE2MpytQjB38iIuueMCqtTOQtNCj1GNKjXqn9jK4hOGMfz+EBjA8xeB2a3jK6RrFmRNRyjpSOlCFjwFju8BCUoW0nY92N8GNL/uUKxibm6iNwzQwP4OMulm/euIOySH/l6kZxUyf7Q/A8gAxubogmeHHuhSgqaBzyNQDRI1xOPJMuw6+TilN0rNNhNKmLTEw4lltnu0bPpra5BDB/C4vGE7ESmqwsKpeh7/ZXf3omrdKqjG0NnElpXbKThQQOXaWRE/l0JR+PKF73DYnfy7fhfzpywOsiGaQy/ZmC0Lj9PDN6/qwpzFhY4ylSZBd+zjh32Iw+5ECMGld13I5H3v0+XqDgGRMK/by/5/s3m6/8usW/wPDrsTrzd0xql5fYEQVYNWp1OjfjUMh/28DEYDl91zYZl2nUiklEitCBmpi/0RIowNwNKTQwqPACZ0B1l6suAFrVCvwARk/ghwTPUf49E3OIte1PPHpR096yTcCiASZfydSQfSd0BXRjQ2J/RDbQDLBfqh3p3InBvBu45As2nPXyBSADMSG8WFCnnZBu7u1YDbuzVk7Z9JOOwKblfpca3I4o/RDl6Ftr+DngJZns3TCsgp7dQ7XNY2rNMsjSXJTM8bjv3O9bqFG4N0KcqiZFZrTbYy7s8xAd31w3HaXRhNEdKsAK/bS/buXH7+6Ff+XrgxJicNet/Upp0ak1U9U49rRzlN02QgDbFmw2qYrZEraEuz+a9tjOj5VOBe8w7ks+C7P0NWJW6Hmy/GTKH9xa3CVucKVaHdxfpKSwjBmJ8fpcX5TTGaDJisJqrUyeLpqSMq9ExduhYisy9A7m+n51TnPxJXjReR9iIi9TEwnq2nSFr6AOE2jZ3gXoT0HfQ3q4h1Jh6LKynrGB/Y3/Pb+xyI1EOZLX45XJLuQit6F3kwXDGWB2QBZIzHa3mYMffUYcr7lXj5u828NXsjDZvbmTctjY/HnhZ8TtE7ugiZlg2uX5EH+yM9f8d43xWPU9qpp2Qk89jX92NJ0vXMTVY9RU81qiiKwGwz07nfObTv3eqY25JZLQPVEFu0y+3w0KpUD1CLzRx1Rr1rY6QUMR29CcVyKlXPiKkluFAE3a7rzNjZj/Hxpje4/907qd2kZsTjDSYDzc9vCoCqqjzw/l36KilM3nhppCbZuvpf1vyhz4yyd+ZgNIf+jKSEHRt206htfVp2axokFWCyGLnkzguoU8q+9MppPP/To3y5510+2vA6k7aMP+qm48cS6dmIzL3DX2Tknz07fkDmxbNSVIClFyLzc5SsHxBJNxFea1wFtbY+Kw8jnhURU3uw9tUfFpZLCU6/RP8+ZZR/Jh0l9u34GqkV6GmcWT+DqQeIKqBUhaSbIPtS/2phH2E/zMKIkG7M6f2pf7aVa4ccwJasYbFJLDbockkedRqWflgevlqRgBNZGDkNuKJzSsfUQVc8/GrPuyyduRKvx8fpzeuw7OeVFBfoKY2N2oav1oy7HRe3xGw14iiM3q4OQKiCGRNmMeiZawOx8GZdmrDoh2VHdnEBuzbtxWwxImPw6iazkUHPXouqqqiqSterO/Dx419GPN7r8eqrBT/n9GnNuD9fYOq4n9i7bT+Va1bipw9+CZvfrvk0Nq/cRrPOTahevyped+hyXlEVmrRvwOIZy1k+e1VQzFxKSafLw5dnp2Qkk5JRVsOFE4fU7EjHVCh+n9D+oy5w/YH07UGoR7fCkK7fkQVPgm8vYEBa++kZJIYzwLue4A1Jo56ep1SNUPAUBmFD2AYgSkIjUiKNzcD+jl+AS89+wdQRqTnAPi7KWEbw/YsUZ0HeMPAsA1zg2w+Fz8Zws3phFcA19+7DZAz+zFlsku79ykqhleCJ1AKv4nPKO3XQQxid+54T+L7OYbPOHRt2kbMnj9Ob1zlmTsBoMtJ3aB8+GPV5aBHFYWheja9enMq3r06nw+XtGPr2YG5/aSB//riiXA0pAkjYvWkvj/R+HrPNXGahz9AJt4ekP9ZvWY+d/+wJv/8g9Q3XzGrp1GxQnR3rd1HnrFrc88YtgRS1Gg2r8eEjn4ekb6pGAzXq67nJthQrfYf15tvXZgTi/kLocsLXPnIlD1/0TEgmk8fl5e37P+bNxSdXByDp24c82Be0QoK72JdCmMC3E47CqUv3Sr82eclDwwuOyUhZiMh8D5l3P7j/BBRQUnXlR79olkwaBPaPS9knAOOhcdAAGxjbQqmiISGE/mA4LHdbs3/kd+hRJjbSjVSqQf5I8Cwo591awHxeQG/dZAzf/D24v7kg7Iy/gjUfKQ//aUGvgoOFPHrJGLas3IbBZMDj8nDVg5cy8In+x0QK9vHLx5ZbN8ZgMlD3rFqMX/oCG5Zu5qHuT+qpf1Ji8EsBxHujt3H7+qRWSmHftgM0P+8s+o+4HHt+MUPOeSRETiAEoW9KGowqdc6sxdjZj2FLsWLPt3PDGfdQlGsPPNRUg8ppdbL4YP1rSE3i9fgwW03MeG82X439nvzsQs7q2EjP1396MuuXbAp7SYPJwI/Oz8t9nxv+3MTa+RvIrJZOh8vaRlXTjDda3nBw/kj0jUYzosrvMedQh71O7p3g+oVQx2VCVJmr9/LUckCzg1ojSDpASol0fA32d0HLBVNrMPeAwpf02DUSlFqQ+SGKIXJ4LjDW/nN0udqImEGtoY+thZeiiIxND/tYOiGMZyPUqmjZl4O3jNi44UzwbiF4pWRFpI9FWHqV04ZjTyyCXv9pp/5gjydZM29dUAWiJcnMAx/cTderzo379f5321v8/OGvMTWYLo0l2cILP4/mzHMa4vV4WTRtGXs276NqvSo8N+C1sGmR8UI1qliSzFx2Vy82LtvC9nU7OfDvwZjP7XXT+Qx753ZAXxH975a3WLf4H4QQtOnVnDteHsjEJyczb/JCfD6Nuk1rMXzCHYGwWHGhgxtOv5vCnKKIK5ysGpl8vuOdmO/J5/XxRN8XWTFnDZrPh8FkwGg28vJvT1LnzNh6th4t2r6W/gySSFjBeiVK2uPlGle6VyALnwXPOlDS9fx0mRN6oEhGZE7SNcdjHdu7A5ndh+CZtqI/DLJmRdWSkdKL3HcW0Td1LOgrgCP5PAv9n7DpIRjrlWC+CPJuJzS0VQq1FZgagOM7/V5QIekmRPJtFbI/aUKlMQo5e3NZO39DSEm50+5i8suxlQ2Xl0vuuACD6bCIl9CXq2Zb5FmiQA+fgD4L7nRFe6564FLqt6pH046Nwm4uxgufx4c9r5jPnpvC0pkryd4ZxkFEOXf2pEPiTbUa1eDVP55hasEnfJvzIfe/dycv3Tyeed8sxOP2ovk0tqzczoPdn2T/v3qjhN++XKALmUVw6GabmWsfvqJc9zTtnZ9ZMWc1rmIXHpcXR6GTwoOFPNnvf+Ua5+iI8jtTqkHKUETq6JhGklIiXXPRcm5D5lwHnlXoKYgH/Pon4U5y6xui5UA6viS0eEjT4+bu6CtQIQx6nD4qHo7MoYP+sND8Al5uPbfetw2R+TEY2xAxfcu3Vv+/yiKwXq5fv/gD5L72aAUvhmSsSc2O9G7XC6QqKP+JmHo4ivKKMRhVPGEaKhdkh4/FHQ1ej5epb80MiomrRpWM09J44tsH2brqX375/A/W/LEOjyv4g61pGqeffaihRGFuEU/2fYl1izZiMBnweTWEIo5Lvn15r+E5vJpX0/h8zBS+eWU6Po835F4BPG4v34+byW0vXM/uzXujCp91uqIdl9xZvmXyj+/NCdlXkBL2bz/Ani37qHb6cYinWq+A4s8JThk0gLlbuXtnyoJR4JhO+Fh1pPCOhix8Hen+RVcYNNRHpIxAmM+JcDz+zcMITlfbX7ahKQ9BfrSMnvLkvJeFA4o/QVT+EVHpM6R3q3+Vcfjfu0ufpas1/LP1Ug03iichlXRE8m26uFjhc1D8VaDLkky6HZF0Z4Xr2vWfnanXqF81dNaMnp/d7qL4pzh+MOpzfvt8flDjZkVVuPK+3jRqU58Lb+7GY1/fT1JaUlAqoMlipGmnJkFO/fnrXmPtgg24nR6KCxxoPg2TxUSHy9uWqzjOYFJjKs46GkrSSEv4/PkpfPO/aTiLnGEdOui59VtXbwcOCZ9F4o8pizmwo3zxV2+kzWYh8HqOXSgr6FIpw8DYFL0gyKqHDQz1EGlPlWsc6VkVxaGXYCD0g+EFx0fg+xdwgXctMncwMsyMW0o3Ws5AcEcImUqvv1goOoq1N1HTGeONLAp8KQz1iOzuPGD/gNCfoSOQNy8LX4XirwGXLo8gHVD0DrL4q2Ng+NHxn3XqqkHlvvG3YbaZAk9ao9lISmYy1z5SvuV8WUgpA1orpfE4PXzzyrTA98npSYz7cwydrmyPNcVCWuVUrrivN099d0hTOnd/Pn/9tjYkju4qdnHg3+yg1MKy0HySFt0Py98WxFQRGitNOzUJfC2l5OuXpgZpvITDZDFy5rkNAb2ArFKNTFRD+I+qx+Vh/NAPWTxjOR53bCl4Pa7vgilMgVRaVkpcFDhjQQgrIvMzROYniNRHEOnvICpNK/+mqGseUWPGgD4DjmWF5UQWhjZklkXvgHs54XVbrGDtHcg4kVKi2T9B298Jbe9ZaNl9kaUfBobjVS9gAPN5wS+Z2hF21mNoEiVMla+HYBwTCf05O6D47aM3Nc78Z8MvAF2v7kDVelWY/Mo09m8/QMseZ3PFkIsiNpQ4Urweb4hDL6Ewpyjo+yq1shj95fCIYxUcLIwYNsrPLixXU2zNp7F81qrgFyVITcNoNqIalKihj7IQiuDW5wcEvnc73WUKh5UUhfW5Q895NhgNvL7gWZ7s+xIrf1sb5h4k87/7k+WzVmO0GHnh59HUb1kv6jWuuPci5k9ZzPa/d+IocmK26oVSo74YdlyX0kIIMDXX/x0B0rcHWfwlZW4+KmmgxdjEwRsmw8jhn6GGw3qNXhRUYlPR68GzXu9qZM7NUOkzhLEppNwBudHi7xY9vCE96A+RIwkpWkBJRiQPCXpVpD6CPHi1X7HSgy4CZkKkPuFXhfwndChDA8ANkWLovtiSBo4nR+3UhRC1gE+AquiJqxOklK8d7bjHi0Zt6zPqsyOQMy0HRpORGg2qsXNDaHu5hm3PKNdYNepXDTuTVg0q7S9uxeLpy9lfznDE4SgGlQGj+tLmwhaMv+8D1i3aWKbcQjiq1qsS5GBNFhOVqmdwYEfoH4JqUDFZjLTu2ZzBL91AeuVDHWlSMpK5763buKPVQyESAiU47E4cdicPX/QsX+x6B1WNvNowW828Ov8ZlsxYwep5f5NVoxLdB3SO+8P8WCKlROYM0jdDIyGSwDZQd0z5D1P2jB5Qw6QmRsvScXwOjs/QzJ0g7bkIYQwXsvB1ROYEhKkTUiQHhUYOYYMqixC+rUjfdsi7t2x7w5F0FyLpGoSSrpuv5SILXwfXTF12wNAQpABjE3+hVWqEmboZkeJvz6dUBS1Mq0bjWUdm4zEkHuEXL3C/lLIJcA5wtxAi9jyp/whD3rw1KNSjKAJLkpk7X76pXOMYjAbuefMW/1j+10wGktNtnH3eWeQdiLCMLAdetxeP20OjNmcwdvZj9Lv/yORqi3KD/3CFENz+0sCQTB+zzcQLs0YztWAij3/zANXqhW5U1mpUg/Ov6VjmNd0Od0B2IBqqqnLuJW0YPPZGrryv90nl0AE9w0XbS/jNRRXSxiOqLEdJGQqmLoSXBDgcI5i7I0vJ9GrF3+sx5Ig4Kal+Jf+RCKqoErwb9Awmz0q/7ow59NrpL6MoFr3XqT1a3UH08KAwn3vIoUunXuTl+FLPfdf2642jFStK2miEobbu8LUw+fNqdYT5HL2YKnU0wfsBArAgUkZEteVEcNROXUq5R0q53P91IbAOKF+Tyv8Arbo345W5T9Ph8rbUalSd867pxJtLxtCwdflm6gDdr+vMmJmj6XBZW+q3rMcV917E+GVjee3OCWU2zIiVz57/lkcvHYOr2M3gsTdwVodG5R7D6/GFpCJ2vepcHp/8AA3bnEFKZjLNOjdhzMzRNO9a9oxn6NuDy9aTkfKoQkYnDdpBIv75mtqjWHscCiUVvUz4rBUjwcqNGhR/iMzugfTt1WPJRWOILSulRGM9wkazWgOZ3QuZexM4p6GHP0z6Pah1Eelvoli6HTreG77BOHBY+7qQN4MzcRzT/R2fStvlBPdSpMcfznNOJ+x+gW8nUtMnScLSDZH5PpjO0WftpvMQlb5AmGLvEXu8iGtMXQhRF2gJLA7z3mBgMEDt2uXLjz1VaNDqdJ745sFyneMocvhDE8Gz26YdG9O0Y+PA96vm/h1V9EsIgcFswOf1ocUgNSB9kqU/rWBo59H0G34J3a/vzNoF5etc73F6mD5hNs3PO5OFU5eiGlQ69zuH1hc05/TmdUlKs2GxHT5ji4zBaKB971YsmbEiKIuoNI4iZ7k2i09ajGfrueYhWMB8fuA7zf6h3pMz0kzd2BI8S9FFrXx6qMXnROY/hEh7xS9jUA4sl4BzBsEhGIv+EPL9e5gdbsAEvr1I6dUL9r07kfa3o6wOlDI0aVQwHtqMlZ5lkcfyrEFqB6NUuUpKrwqEqS0iM3zTmopE3CpKhRDJwO/As1LKb6MdW1EqSisym1du46Wbx7N19b8IAe0ubsX9793J7s17GT/0QzYu3UxSWhJX3Nebax++nL8XbOTRS56nuCB8atvpzevo3Yi8vpCCq7IwWYx6z5ojWAWkVkrBaXei+TSEoqD5fJitZrweXUu+23WduHfcrTGX6Ofuy+O+jo+yd+v+iAVJ9VvV462lY8tt6/FEarng2wNqbYRyZHpDWsGL4JhUSoLWBOppiErfI5RkpFaM3H8u0dMdI2GArLmQ3ZWo3YpCMIOxCXj+AYpBrQNJt0PBE0SX8bVA5heQe4PfCUf6jEbQagFABfPFiLSnA31MtaIJUPRG6LVFEqS9Avn36/rw4a5jbIdSaWIUm48/x00mQAhhBKYBM6WUZWpWnqpO3evx8vVLU5n+7mw8Tg8dr2jHwCf7lztem7svj5sa3hvUks1gVKlarwrZu3KCwgtmm4meN3Tl7tdv5upqt4Vk05htJm574XreHTGpTCGvE4HJauKsjo1wO9xsXb2D0+pkMfDJ/nQ8THnR4/aQuzePtMqpzPl0Hm8OeT9inrsQgp88X5QrE+h4IaUHWTBaDwsIoz7rtA3Qm0hHKbMPP5YE189I+8e6Xor5AkTSTQhF/7xJzypkzk0RNiXLQkUP7xxJOM+i9xtNHYkQBqRnnV7pGm3DVSTpG5ielcQW/w+Hql8bHyTdqme/aDnI7B6HXVvVW+elPgd5d0b4+ZgQlWcfVVPuY8FxcepCD9x9DORIKWNKIzlVnfroS8fo5ef+DA2DUaVS9UzeW/tKzGGGJT+t4JXb3iJ7V+iSUFEVf3ec4N+Z0Wzk439e5+37P2Hu1wsPvW4xYrGZKcqzH5dq03hhtpkZMu4Weg08X89t/99UPn36G3w+vYVatdOrsG3tzojnW1MsTM2vWDOsErT85/zhkGABKVKGoZRKDYwH0rcbeaAXsTe6OBKMhHf8JsRpfyKEVX+Q7e8QORccAJs/lbGc4Z4AYWbwxg6IjPHg24rMewh82/ymtUGkjdVj5rm3hn/YGFogMt5CqJWO0J5jw/HSfukI3AB0E0L85f93cRzGPanYsmo7K35ZHZSP7vX4yM8u4JfP/ohpjLeGf8io3s+Fdeigl+iHc85Gs4EnrnyRRT8EPyg9To+uingSOXTQC6neH/kpUkpmfvQrE5/4muJCB65iFy6Hmx0b9kTt4NT9us4c3JPLZ899y8uD32bOp/Nwh8nrP55IrRAtd5hexRmuiMX+ftyvKdTqYGrFIbncaJQcYynjeBsk3wOpz0PlaJrjbqR3s26HMIL1xjKu79M1b46YMJ9xzwJ9Y9ZwJkrl6Ygq8xBVFqFkfoxQT/NXwUYI+3nXIw90RcsdggzpsFSxOeodJSnlH5xqnVuPgI3LtoQtXHHaXaz+Yx0X39o9zFmH2LttP1Ne/zFqrYVQABmq8eJ2eti2dmfYzJcTocIZDwpziigudPDZs9+EVKBG2iQFPd89rXIqgxrdi8/rw+308OsXf/DZc9/w+sLnSEq1xdVO6VqMdHwF0oGw9Na7C4kw3ZtybwXPmsgDaUefihoOkf663kHJvQR9DhcuV90CyXeA7wAY6upt7DwhuQ4BlGQ9f1w6ZiCjZcbYP4F0fW9DGCojMRHcZagEFVJHI0QyMj/ONSOe9cicgUjvRl21MukWsPbT0xSFATLG+2frJU20S+7H/3Ny/YrM7o9UUkCthkgaiDBW3C5a8B+WCYg3p9XJCjt7NFmM1GwQPS7n9Xh5/MqxZc6oG7erH7KhaLaaaNK+AWoZqX6HYzQbjm/1pCLClvpHMsFkMWFJMpOzt6wuNcGYrSamT5iNo8gZeMg5i1zs2bKfr8Z+X267o6EVvo7MHQzOH8A1G1kwStdPkcGOTnr+Bs96osanj5GjEEoaSuYHiMq/QOZX/pz10imBVrBcgJJ8F0ra4yhJAyFamp6pc+BL6ZxJ1Pi38zu0vU3Q9rZB2idHOMgASfei2K5GymPxeXTqDyiZA74tUPB0kBSCMLVGVJ6HSHsMlHChFjf41oPnT3D+gDw4QM/dr8AknHqcaH7eWWRWzQhxXKpR5aJbos/Svxz7Pf9GiRGXjNPv/ksZM/NRzmhRFwBbqpUrh/Zm0LPXxjwjV40q517ahud/fJRJ28ZTt9nxSS+t36IeJqspyIkLIajVpGZIMZLRZKDv8D6oqsoZzeuGHS+zanrIeULo+wjFBaEpbB6Xh1+/nH/U91GC9O0F+wSCMktksa6R4vo9+GDfv0RdzAqb3u7tGCLUKiimxoiMtxFpT4CxPZg6INKe0+PLfqTzV7BPijyQZxHSOUf/Wkmm7EW6DygA3yr0XPHShUMqKJUQSQPRisZBQSw9WY/E8Zf+23BC8XtorkOhSqEkI6xXEnWZHBjHCYVPIsOmk1YMEk49TiiKwv9+e5JmXc70N10wULtxDV6c/TiZVTOinjt9wqwy0wxNZiNuh4emHRvz9vIXmen9ku/zPuHmZ6+jacfG1GpcI0R1UigCg+nQH5HBqJJxWjrnX9OJJuc2pEqtLJ79YWRULfd48c/yLTgKnUFyA1JKdqzfFRLv1jSN3Zt1/fjBL96I+bBNZrPNxD1v3spDH92DLcWKLdWKJcnMaXWrMPqr4RElDUzmWGLLMeJeAGHCLFCMdM0JfCe1AqT9QyBcrrQAtZGeheFZh3QvPSbhMik9SMcMtPxRyKLxenFSpYkomR8hrL0DWTeafRIy73YgSpaKzEfmDUd6NiKsVxNaGRoNDd0xWtBdjwmMzfQZf9EEYst6icfPR0LuLXpaaWlM7YnNJUrwhtGJiXaGewla3kNoufcinTNDVnPx5D/d+ehYYc+343F7g/RLotG3ys0UZEffRDxaYQAAIABJREFU9TeajUzcMo5K1YIfEC6HC4PJgKPQyet3vcu8bxah+TQat2/A7S8N5JfP5/HbF/MpyitGCNCkxGwxYU228Or8Z6hW7zQWTVvG89frcj2aJnEVu0745qrJauLNxc9Tr2ltNvy5iQ9Hf8GWlduoXr8qNz7Rn1Z+dUm3y8PGpZuxJJk5o3ldhBDc1XYEm1dsDeowZbaZuOX5AVwxJD57+NL5MzJ/RJjMCRVsN6Gk6uXjWs4gfzz78NCLANLAWAc8G/XvBaDW0ZUbldg+O2XaKZ3Ig9fpoQdZTKCKM+0Z8O0A316E6Rz9YVLwELE1qVDB2g8l7Wm9uKnwpTD3Fyv+jkUxpzEa0B8KR5KmWRozpNwflHEkvduRB68sI08ewIjI+glhiK1Lllb4KhR/6BcSk4ANzOci0seVO401luyX/0Dp3fEnKS2pXMef06c1cybNi7gBaLaZuXbk5UEOffmc1bxx97vs2rQXRVGwpVqp2bA6D3x4N537tsdkNpG9O8efBqkrMpY8wB1FTpx2J2NueIPX/niGc/q0ZvL+9/l74UY+fWYya+dvOGK5AaEIrn34Cr4YMwXNd+QPBs2nser3v5GaJGdvHve/dyeVa4bGPE1mY1BlLcDor4YzvOtj2PMdaD79Z9qmVwsuLWczjaiYuxJ+VmdE2PoCIH37/BrkYX6WIkOXhnVOI7B5KAHvJmTBk4j0Mss9YkLaP/UrL5ZskPqvlf8A+DcupWMq5es65NMbYgNK0iA0tZZffOtItOgl5Zt9GyB5iF/64GhSNV3g3Rr0ijDUgUrf6RWtjhlEXLGotWJ26NK3y5/ZVNrWYnAv1Fd75k5HZH00Ek69AnDzs9exdOZK7PnFuIpdGEwqQlFo0r4BVWpncfGtPWjW+ZAu+aYVW3nssjGBYiKf5qMwp4h1izaydfV2/lm6mb7DL+G2ZsOx54cvkZYS/l6wgS2rtnP62XUwmowgYd2if45KP8ZsM7Nr096jcuigx8e/fXUaEx6aiNQkHpcH1ajS5oLmDJtwR8iKpTTV6p3GpC3jWTZrFdk7D9LknAbUa1Yn4vFHZp8ZMt7XN0pLnJn0Qur/2TvvMCeqto3/zkx6spVdOkhRQKqCIohSREQUFRsqVhTF3gtYQUEs2DtWUBQRBUWxgIigqIBI772zu2xPz8z5/phsySbZzcKC+H57XxeXZubkzJls8pxnnnLfTyBMhr4qeq4RoolF26okg3820dUgQfD9iJQ6QijIwGJk4VgIrQORAs6hCOdNCXl4MrTZ8BDjsjOWXLu6JXs2sJQzRu5JHLwMXWWwGrTB0h2uTgmC/XKE82qjvd/zLgcdjhEORAzKY2FqgkgZi7Sdh8wbTvRno0Dah4lfx/87MTd/6UH65iAOg1GvDb8cJXAXevjpo19Y/ft6GrdpxMCbziSjUezGh6cGv8CCL/+KG38128x0P++kiEakeMholM4xbRvTpE0jfB4/P34wt1KaXZPFxNlD+zDnk/kxibMsNnONkIoJRaCoClqMXINQBDc+dzVnXnk6afVSD/lahwIpg4Y+p/SD5eSIln8pA8isU+J0Upb4U7GMoYKotwpCG5AHriCKR8VxOUoViVW96EVwf0jNNx6ZDUObPgXF1BQZXIc8MIiD7wKNBQFYjQ3SfiGy8EnwflruvApJD0PRcxzc/akgXEb5pkhCOIaAtW9UNZhe9Aq43zXGowMmRPpHMTeDeJDe75CFj8b4DpjAOQwlKb52QiwcMZqA6uJ/2ahrIY0V89cQ8Abo0LMtjqSaVyQf1v4etq+JXy3jSLYjdVmlIEVFKKpACKXSOnCzzcz7q1/Cardw84kPUJzvIegPIoTAbDMRCmiVEovVJCw2M7e9ej3nDDuzWu/Lzy5gwgMf89v0v1AUhd6XncqwZ67ClVq9sFki0N1ToGgcsb1hhejwgwDzSSh1JqPn3Qr+n4n2Rq2Iun/E5IyR2l5kYGU4vFK9v3/lsBrsiLLI+H9CRvgouB707TV4HUCkgutOFOdV6IHlkHtprEFg7gbBv4ld+x4eg4qxgYYMKgKphJtPvZR+PsIO9stRkkdGzSC1feGkeBJYexpPaNWAHtwCB84hetOzIjK+CcvsJY7amPoRxvrFm3j43KdLpea0oMYdbw6j/7V9qnhn9dD65GPZuX5PXOMpdYnJaqp2LskImcQ36EIImrRqWMp3PmHFC8x4dRaLfliGt9hL3v4CAt4j17kZ8AV5464PObFvh5gc7LEQDAS5s9vDZO06UPoU8NNH81i9cD3vLBtf43wxivNydCGhcDTRP2yJ0b2pYhh9m6HEU6JTGlpPzPCCMIG2B5RWZTOFtiLz74TQNgzvP97f0crBebcybAg1Sit5/PM4LGEXmQ9Fz6MjwPdj/PWYW4GpMXinETsME6YOsPZBpIxCKGlI7zfIgseJ2PCkFzyfIp3XGl245WdQ64P9ooO7DalB3g2xT7oerLZBTxS1JY01hIAvwIj+YyjMKcJT6MVT6MXvDfDare+xfc3OGr3WFSMvjKmxCQY/TFr9VPpf2/ug51dUBavDWqqwpJoV7C4bdRql8cSX95eOS81M4arHLyXgC7J/Ww7u/MrEFA4PdE3n16lVh5lK8Pv0ReRnF0aEdYKBEPu37WfJj0srfa/Uso1wQzxpszgQamPDS4ye0aDQTbofbBeC6y6DRMoU5tg3tSJmXbYMGYRUJS9lwCDMCm0gsiuyIizguAKUg5E7CBK9GQSo2bBLeXihaDQE/4w/RD+AkjIW6i4F+8VE0xvogAb+uaV5Den/lZjlpcIEgb9raO1hBH43NqgYXnrsEteaQa2nXkNY8uPymJ5zKBjihw9/YfjzVXFfJI7GrRry8oKnePu+iaz6bR1aUCtNrjZt04jR0x8grX4qP038lcIDkaWSQommGagIXdPRQhqd+3XkxmeuZOPSraQ3SOPEvu2jZOIWfr2YrO3ZMTVTDwWKSUEoAi1QeT2vFtT4/etF6JrOsSc2p0u/jpUKZ29esT1mWCrg87Plj4c4+YzRUckrqReFW+3/NJgVkUjXAyjOK6PmiQlzh9jJUmxg7YvivDr2+2wDw95w+c/ADo5LIkMv/l/KlctVBoFw3WJUZPj3JDC+PGoiTGvF2KRqKCxkOw8ARXFCyjh0kQae94leqzA+I8cVoGRQGo4pD+k2avjVptWKmVcKbQ/ErEf3G+Wkhwm1Rr2G4C70oMfIT2ghPYoOtybQslMznp/zRPgaGttW78SRZKdBi3rs25bFD+/P5eonLmXDks2GQIVFpd9VPZnz8Xzycwqr/I2GAiFW/LqGgC/IWZV4/Wv+3Fjt2H0isDmsUZwvsSClZN2fG1n350bMVjMpGUm8+OuTNGgROxzTpFVDbC4rvuLIuS02ncbNC/DvuxEt5Xucqc3KrpF/r1GCRrBMmKLoOaSpCcLas8o1CiUV6boV3O+U4z63gpqBcFwW8z26ZzoUPkGkl6eC8waE67bIwVpWnE2j9O4AAclPGvFqy2mGkTssFSuVwNQCQnuoEaOuNEWxVQhrinANfsUnFVESWwfhGIz0fEbMe9c2I3OvgTpTDEm9Q4W5Y+zjwoGwdDn0+eOgNvxSQzihT/uYCUaby8ap5598WK+tmox2+gYt6jF57JcMbXMXr9/5AW/d+xG/TPmdBz68jWn73ueEMzrg9wUSdroCvgALv6lM+R0aNK9bA3cQDW+xLyGFpvII+oMc2JvH6EvGxx3TrkfrGLzyEleyxin9CpFS5/fPHik9owfXQGA+0bXmXqT73YTXprhuRaS8DJYeYGoLruGIOjNiJzt1T1hUoqL3bUGo9RGiwpOI5QTih0EU41qZPyHs5yJzr4biZzEM3xHm4QttAtOh8JOrgBMsAyDpEfT8e9H3d0HPOtWo9rGeRUyGSamDzUimC1NLSHnemCcmfMjiNw5hjWUQ5rZgPYVIbVMzKJlgO3xEtrVGvYaQ2bgOlz04CJuzLDtuc1o5vttxnDKw8xFZw/olm/l49FRCgRC6pqOHdEKBEE9c+ByXNriBCQ98XK1EphqOrVeGM4bUfJ0tcNAdrVI3qAeydmTHPP/m3dE1xkJA+1OKUU1gtUmKc7dTlFdslIzm3U7cXVDbV621CVsflPQPUTJmoLhuLxWziELwH4NbPApepHea0dRUfl5zB4hXlSEcCGtfhNoA6f7YEKyWHqrf9BMxKQf3kB+sdnt9GWzguB7UOhD4BQqGG41bssgQlHZ/CMXjwXUXRpjHarwHKySPRSjppTMp9v5Q51MijW0JJITWHOQaoyFS3zSoitWmhrap4ypEnWnVrqKpDmrDLzWIa0cN5oTe7fju3Tn43D56X9aDXpd2j4pDHy58/94ctDjebf7+QvL3F1ZrPsWk0ueyHpWO+TfoBOKJhZQ/X7FWXtM0Vi1Yy5IflkW9T0rBL9PT8LpVho7Yy4o/U+l2eTEu5+awwHMsCMPrriakngeBv0A4wNINIWIkvIWTuMnO4Apkdl+kuQMi9VWEmmkctw4A33SiDLV0Iw9chlSSDY+1RuLZkoNPkB7s+0xGlYvMJ/Zm5IfA34ikB8B+NvjmGvkP65kINSNqtFCbIONtatIQTK8JFlMhzAjXTeC66ZDnShS1Rr2G0al3Ozr1bvevXHvfttjeaWVQTAqqSUULamEdUYHFakZKye2vXU+DFvUI+AKoJjVmAtJd4MFitxDwVp+1zpFkw1NUTSMjDN3T/Kz4/OOuVCeNjisTXNiyYjsPnzMWd6E3gg+m4sSL5iSx8k8nqimFes0yDa9WqHEcWhXhujnhZUttD9LzudEyLkpCBCZIey86MWfuaFS4xIQOBCC4DJk3FOrMNLjBXbci/T+W88JLrwz4Qc+mZsMtR6YXoQzBcFdpZYIDAkLrEPYLIV7yuWSo4kLazglvhBWg5xr175ZKy8GPWtQa9f8hnNC7HX//tDzh8XaXjdMv6cawZ67CardQlFvE6oUb0EIaXQecyL5t2dzS5UG2rNiOalLofVkPbn/thoiGqnrNMnEm2w/KqFfboANI4hp01aRgtpoZ8cmdpV6WFtJ46KynKt0ESqDrCu5ChWPapjG09V1YHQrnXeXgnKuKiSxfV8F5S0L6lTK0I1w/vpHSuHw52laZex0ycy6KWp72IEDlhFIY50M7IbQazO0RpqZQZxqy6EWDb0ZqGI0K5Y1vTT1VqQmsr6bhJ6HErloNKmlzZ4MLP2reANL3I6LWqNficGHXxr189vRXrFu0kcatGjLk4YtoffKxUeMuumcgk0ZNJRio+svvSLbz5IyHIp4qHEl26h1jJD73b8/mgTNGlVa26JrOvM8XkrU9m/G/jC59j6Io3DPhZp4a/EJcIejDDaEKmrdrymkXn8KA688go1EdcnYfwOcJsG9rVrU3nPLdum893oDVix089Nq28BEzKHURzqFVziNlCJl7JehZxDeobsg+Dd11J4prePiYEv5XhTcsVND2g7m98dLUEpFmJPn0nAsgtLbKNR4cjrRBT+S6JlCbGIY6DqTUgWBpPFso1rAaU8XvrSAxCcCjE7VG/SjH1pXbuavHo/i9AXRNZ+e63fw9ezmPf3E/XQecGDHWYjUz/pdRjOg/hmAgRCgYip/jC+m0Orll3OvOeP37KCMd9AdZt3gT29fs5Ji2ZSx1xxzfKKGNJC5iaAZXB1KTtD+tDVc/dilZO7K5resINi/fZnTWmg8tnxEKwLwZKVz1QDsaNS8GWz+DUCtctSKlhOASg/9FSQfbOWUJ0MDvxqN8lTcXhOI3kaZmCFt/hLAgLT2M91fmncpAfMUkU6twR2qiYRI1/O/oFX8wvigWopugBFh6IVKfjhkHlzJgqB15pgABpHoMInkUWPsAj8e4jgVhP7+mF3/EUFv9cpRjwoOfGOV94cYmKcHvCfDabe/FJPRq270107I/4PEv7uOuN2+kw+mRtLQIg1v85hevxe6Mlf03sHXlDmNTqACTSWX3xsiqjycufP6QjLLJrKJUU46vPOwuG8ee2JxPxkzjulZ3smHJ5tIcQcAXPGSCMV2DxX8MQ8mcjZL0IEIxSMSkDCLzbjT+Fb+KLBqHzO6FDCwzzmu7SZxn3It0v1f2MnlMWF7NiuE1lvCOl8AGtvON8rgwpO5Bd08yONxlMYl7m4qRuE2fZCRcj5hZKKFISBQ2cFxGtC9qBcWBUGIzd8qCR8IG3QfooG01GBi13ZDygjEvDkqrZVx3IcxtYs71X0Ctp36UY80f62Mez959AE+hJ4q7PW9/PkvnrMTmtHLWtb0ZOPwssnbm8P37P7Ny/lrS6qcy6PYBtDu1daXXPb7bcaycvybKIAYDIZq1L/PSi/Pd7Fi7+yDvzkAooGFzWmOyPlYF1aSQlO7infsnRWx+lSGRrtqKiBWTl54vDQ+9hKwr3Fgk82+HzPmgJMa5XQotx3i/thvyrgG9pBtYgqUXmFqC/yfQ842EqO8bZOB3SHkazJ0MgQdtH4bxUgATKPUqCf8IINkQbEi6D6kXhhOqdozN6HB77UFQ24K+i9InChk2vLGeMIRi0A+jEvkE4wPfT8jQziiec6nngu97ou8lgCx+ByXtFXT1E/B8ZpSFOm9ASZAr/WhFrVE/ypGcnoSnMJrhTzWpUTXkU8d/w8THp6CaVIQiEEIw5tuRtO/RhmtHxe5cjIfzb+nPjNe+JxgIlRpAq91C13NOpEGLeoSCIUxmk3G+BhJwiXSPxoIjxUHOntwqG5UUVaFjz+MxWc30vKQbLw57O+FrCCFib4K+L4nJviiLIbQeYT0ZmXBS0VQqmCDzbjO8yPKGLfAXwn4eMvh32HBrxj99LzLvVnAMNtrSS41XuEpGL4TMBZB7fbg13UsZte0jKOGOVr3wGfB8UGFNJZSzh7FsVbEgMhYaFAzSC5buyOBKyL8fZEnoygSYECnPIz1TiElIJsxGuKmiQdZ2GZ2mUZqiOoQ2ohc8Dt7pGE8rCvi+R6Z/jDC34r+K2vDLUY7BD56PraJGp91C/6F9MJnL9uR1izYyadTnBHxBvMU+PIVe3AUeHh04LkoDNBGk1Uvl6e8foXGrhiiqQeh13i1nkdk0g/OTr+Yc2xCGdbiHHWt3kV6/BjjND9JuuAs8CXWeqiaFYc9ezbhZjzDg+r4c07ZxwtdIquPipP4nJL4oGUL65xnetGMY0b6TihEbLoEZhMsoSwztgNBmoj1VL7JwHARXEx3S8YNnMrE9ay8EFiMypkHSCLCcDrZBiPSPSw269M0Bz6QY79U4rAYdwqWbJoS1p5FPUJJRrD0QdX9HpH0AjqHgugOR+QPCdqZBNRCza1QD1SAqk1IigxuRgX+QSn2Qsb7/qpED8X6NsUl4Dc5zmYfMG35YtGKPFGqN+lGOgcPP4oI7BmCxWXAk2zFbzfS4sCs3v3BtxLgfPvglZuxYSsnS2Suqfd2tq3Ywsv8Y9m/LMrpTdZ2v3/iBb9/6CZ/bj5SS7at38ci5TzN07BUHfX+HikSpBJIzkljy4z/c0/Mxnr7yFQbefFZMwW2hGHFrs9VkiFkfk8mDH93Owm+WsGVFBd5w28UYoYqKCELx28isXqAeA0kPhImkVDAdj0ifiEj/CKxngKkNOK5EZMwEpT4y8AdxPXuZQ+wYvU6lCVXvTISwoTivQEl/HyX12YjaeOmeWPn7DxkWsJwR+1RoU1jSrwwytM2o3LF0RUkeieK6pZQSVziuiiH4bQbTcQjz8cjQTmTOOcgDlyDzboCc/mA5mai/k7CCnkfsJ608Q2nqP4oaEckQQnwADASypJTtqxr/vyyScbjgLvSwd/N+MhqnxxS0HnfVq8z9dEHUcUeSnbsnDMeV4mDhN0uwOiyoJpV/5qzAZDFz7k1n0u+aXhE84jm7D/Doec+wedm2KtclFEHPS7tTkFPIsp9XHdI9Vn0xSh1HIahUoakEJouK3WXHZFZxF3gI+AxBD4vdzOAHLmD1wvXsWLOLY9o1YeDwfnz9+g+smL8GkDTveAzJ6UmsXrgek1lFC+kc17k5Y74diTPZga4H2brgXOo33oHFpqMoYe6oCFgRGd8ZdeRVQC8cC96p5Ui/agiiDiipxry2/gjXLaXJXgA9Z2CYtvdwwAzmTojkR8IqTjF6E8xdUep8ggztQubfAqHt4aYvxSAws5wIli6l3bcy8Dey4OFSnVSsvREpT4NIRuacGR26wgqOIeCbZeQjLCeA/UoouIuYTyLCiUirnsLRkcIRUz4SQvTE6HSYVGvU/x38PmMRz1z9alSy0WIz06lPe1bOXxMzEWlzWul+/kk8PPludq7fzZjLX2Lnuj3VotJt1q4JIz65k7t6PBJFlpWU7iIU1PAWHZqh6nRGezr1assP78/F5/VTnOuuPCkqwGKzcNsrQ9m1YQ9fvTIrShrPkWxnWtb7mC1mQsEQ17a6g5xduZXO2+qEAGdc3owL7x7O3CmreeW2GRzbLpeLhmdz8hmFWKIoPUyGik8V3acytAmZcyGJCFhIWbZ56Lrx/5V3tJeveTcbRj7pbqP8z9wZWfQs+OdUed3E4cTgCzeHE7W5Rsxbuon5pGE6AdLegQMXgb6XqNCTcAACkfIiohwzo9TzACtCcRivA0sN7zxKOk4B+8UG93oYev494Psu9vJFEqLunwhx9NWqJ2LUayT8IqWcD+TWxFy1ODh0O68Lnfq0xxYuU1QUgdVu4cyre8U16AA+t5+FMxazYckm7u35OFtX7KiWQVdUheO6tKBlp2Y8+vl9OJLLHnPrNEjjuTmPM3Xvu1z20CAyGqfjTHHQsGX9apcwmswqdRqk8+ofTzP6qwexu6ogRJIQ9AVZ+PVifvvqr5hap35voLTRaNGsfyjKLY5r0B1JGi99s5Hnp63jrEE/Ig8MIt05jqDfz6pFLpYvdCFlLMuqx/S8pXYA6Z2B9H6L1IvBv4BE49e/zEhh12YLuVkmFnybTDBQVft/+XsKgtwHhSOQBSOQOedCuASz5uAGpTngBH238VrmEzt0ZDIItLJ7hMfG+Pylx+Cwyb/LkJcLQyhppQYdCPcExPkbaFmRh4Kr4y/fdddRadATxRGrfhFC3ATcBNC0aTVaeWuREFRV5ckZD7Jo1j8s+PJPnCl2+g89gynPzqiyVFAimfn2bPy+QKUJIqEIFCVSw9RiM3PFyAsBmP7Kt6VSfgC5+/K4v88oPlz3CsPGXcmwcYaoxLbVO7m96wj81ej0XPbzSlYtWMcbd77PNaMvI5BA96qUkn/mriqNk1eEFtRKw067N+2rdDO767mdHNvBi8Vaxj/Stoubwbft57NX6rPg2xQCfoHNLul7cR7HdSzjTRe2vhFz6e7JUPQMRsJUAiGwdCYRHysYgJfvb4LfW1bfff/LOzh9YAE2R0WDmIIR7oj395dAIByrr2HoWyirnqmIkoqgkvOJxvM1pHcmwnVj7NOWznGSovZwo1E5mI4FbTvRG6kFYb8gwfUcnThiiVIp5QQp5UlSypMyMzOrfkMtqg1FUeg2sAsPfHgbt758PS07NcNmt1TJNqeaTOiaXmWbf1Kai3Nv6kta/VTMVhMdTj+eF399kiatG7H05xWs+m1dRLJWSqMLdeY7syPmqdMwjW7ndYlrbGNBC+n4PX4CviDvj5xMs/ZNMFur9kmkpuOPs6kpqlLqmbfo2BSzJbZ3Zrbo9BhQGDboZbDYJAOvNVgcc/db+P6TOsx4P4P7Bh3Lp6/UBexgH4QoJ5YgQ5vCBt2PEaLwAkGDuTEBBsU/f0om4Iv82b54bxM+fKYxRYX1QGkA9qsgYw6kvkb1mntqGvFKOUtEKzSqRwwWDHvjcWZV0sF5oyEkXQorqA0Rjgsjx7puNc5FwAb28xFKdM7qv4TaOvVDwMoFa/n6je/Jzyqkx6CTOfuGvpV2af4b6H/9Gfzy+UL8ldSBmy0m+l3Ti/nT/ojwtCui8EARsyfNx+ay0X9oH/76bikP9B0NAnzFvpi0vwFfkE1/b8Fd6GHymC/55s0fK11LIpC6ZOOSLRHHLDYzoXAXaQlMVlOlG5WiKtQPi3yc2LcDjY5rwPY1O6Peo5okQsR+gtmxwYbh7Rkdn1IHv0/w2csNOfP6m6hXL9JLl95vqNozjc+bsG29DUWVaKGyDVHXBT98Vp8WpwxlwA1l15NqY6TiBP3Ia8dWjoOttBFVKk0pSXcizR2Qno+NGn1bf4RjCEJEVr8Ic3tIextZ+CRoW42NwD4EkXTPQa7t6EFtSeNBYsZrsxg5YCzzv/iD5fNW8/7Dn3LHKSPxumte2u1Q0L5HGy576ALMVjM2pxWr3WIkEe0WbA4rDVrUY/wvo+jUux3Hd2tlnK8E3mIfefvy+fbt2WTvPIC7wIM73xOXxx0guY6LO7s/zLQXZx6yQY8Fs81Mh55tI0JHiqqQmhFHhCKM0y46BVeq0ZGrKAovzBvNgBv6RgidAPg8Kjs2Rm/WugZL5ibFnFsoZhbPLoDAoog4cFnHZDzYwXQisWqxdR16XZCPGsMVk7qkx6CukWsQCpi7Rg/+D0PmXY+eMxDpL6v0kjJgiIKH6YoNMZIPUDKmobhuRCixVY6E9VSUzB8Q9VYh6v6DkvxgaSxdSj/S+xV6/j3oRc8hQ9tjznE0okY8dSHEZ0BvIEMIsQt4Qkr5fk3MfTTCXejh3RGTI9j//J6AoQ36wVwuvOPwSVUdDK5+7FL6X9eHpXNWYnfZOKl/R/ZtzcZkMdG0TaPS8MzY70Yy/ZVZTBr9RY0a3z+/XYrf6z9sghpBXzCKcthkju64LQ/FpHDPhOERx2xOK3u3ZsUc//L9TXh26mZMZh2zFXxegd+rsGurBdUEWgXnUyhBzMEXkfk+kAGktQ8idTzC1s/gVY9VHw1GGYvjIvAqBp87AaQ0DLoWgqbHBrh59G7efrwRikkihBldMzHikztJrhNjg5E1rY9rJnE+m5qGxKBrRLMpAAAgAElEQVQc3oDMuw2Z9rbRieqZaAiACAvSdReKs3oi7xWTolJ3I3MvM0ompVHFI92fQOorEdU3RytqpKSxuvivlzT+PXs5Tw1+EXdB9GNtp97tGD931JFf1EGgKK+YjX9vIa1+Ks3blyWvs3Zkc0e3h/EW+2pEVFqoAqmVfM8kTY/zIyXs3FSiLl9urBIW6KkBWOwWkDJmU1bj1g1pdGx9+l/Xhx4XdkVRFBb/uIwnL30BX5x7ttg0VBVSM0O0bOdl+UIXitApyC0h3CqD1aYzeekaklJL4so2cFyBSBqBLBwB3u+I3QFqQtT9DemdFY69G2PKlzEC5OeYWDw3CdVk4pQrviYpLQPd+x0UvwzaXjA1A0tfw+BRw+EX0QhkjNLDg4LF6OyUxUbpop5PwpwzSj0jxBKxQdoh+UkUx8EnO/Xid6D4daISzCIVUXchIqr56cghkZLG2pj6QcCV5opZ+iYEpGZW/sh/tGDymGlMfvorLFYjFt24VQOenvUw6fXTqNs0k0mbX2f+F3+y5Kdl/Dp1YaXhlapQYtBbn+jm0Qnbw4ZOkn/AxJgbm7FpZbmyNHmIPLzlEPQF6HxmR1b+vo5Aufp51aSya/0edq3fw/J5q+n+1UmM/OQuFv/wT1yDDhDwGUlHr1tl77bYTwGKIjBbNB5+Z1s5gw7gA+8USBqBSH4Gae6DLLiTVX852brWRqPmfk7sWYyiSKTuhuKXKG/cKua6UzNC9BucB6jg74m+r8KjQmjD4WsoknsBFSn1Kurjq4Cwg6UHIvV1hAhLFHq+MDho9HyDJ97aC4rGETMOr++PPoYX3K8jrV0Nrhu1RUw5u0rhm0XsiqGg8Zma21ZvviOMWqN+EGjVpQVp9VPxbdkfEVKw2K0MumPAv7iyxLDwm8VMeXYGQV+QYNiL3bpyOw/0Hc19799Km67HYrVb6XdNL04ecALzpvx+yNd0pYQYN2ULzqSyzcFqD/Ls1M1c2aUtPo9hMKv/5FiSpIxG49YNefr7R1j8/T/8/vVigv4g86f9GRE287n9LPx6CesXbyI5PcmQ9gsdvAiEala55alddOtXFH1S+gCJEAre4v08eG4rtm+0oGugqpBeL8iLMzaTarojTmleLBx5wQopdYIBGaPRqjowQcobCGuP0vCfEALhHAzOweWupSGLX6peGEnbiczuZ1ABSD/SfgEi+UlETDHvGBCO2MelVqGy5uhEbaL0ICCEYNz3j9CgRT3sLhvOZAcWu4Vh44bQ/rTj/+3lVYmvXv4uqnZd1yQ71u7moX5PMqTpLWxathWA375ahNlWefK0Kggh6H1BPqoaabAVBRQVTju3aqm5+OWP8V3FG5+9CkVROOXcLtw74WaatG4Us7on6Avw9+wV9LumV5XrqApBf4g3Hm3ER8/UJ+CrsDZTWyN5CXzwxAq2rLHic6sEfCpet8q+HRZefqBxWLEodk6j/J73b3FOSWl8Xw4NAnzfGDwrlY0SKjhvJppjxxam4Y25Qoz6+yLjv96ZSPe7ia/McWWM6wlQGyNMzROe599Crad+kGjYsj4frX+VDX9voTivmDanHIczOc4OfxCQUvLLlN/55s0f8Ln99B58KhfcMaBGSiYLsgvjnvO5/fjcfh7q9xRTdr+Dt9h3SJ6ryaISCmqkZgax2KINgcWqk1432tAqJqOG3Oawhg1I7Nh4PAgh2Fch6ZmU5sRsNUVRGZitZpLSXNQ7JpOBNxv8L4eCoB++nJDJ2qVOnp26GVBBWAy1nTB+/jyLYCDSp9JCCot+TkYLSVRTyU+z7LMJBgRZu00kp2o4kvSYVTCHG1IaDVDWQ3ZYg+CbgfR9izR3RTivMThcRLSfKZw3IoUZit82NgG1EbhGGHMUPEx0fX/F75kPPB9DokLhtnMNnnzvNEqfBJUURNpb1b7LfwO1nvohQAhB65Na0qVfpxo16ACv3vouL930Nqt/X8/mZdv4+Klp3HXqI1E0uvnZBbx88wQurX8DVx5zC5+MmUYwULnx63beSZitlbdBhwIhlvy4nJPPPgGlGk1CYHwuVqeVtHopPDTxTgSC1Ytc+DzG123XZguzPklnwbcpuItUVv0VXXJ2Uv9ODH7gAtp2b4VqVqqtXiSlZN7UhRTnl/GA9Ly0O7E8e6EIeg3uDsANTw/BmVL139JsM2Oxxf8MAz6FtUuT2Li6E9gvQdSZEUEQpcUjYgxXuhjG3BgkKfHKJWmZOnaXRPmXeoqEAIslOsYvZXiNSlMQ9aoxYwiCC5H5dxj/YmTJhRAozqEo9f5C1FuDkvkLir0/in0gIu01MLU3vHbTScR9ctNjhMPiQoYZHBVK/w56ETKwuBpz/HuoNepHIfZu2c9PE+dFhEgC3gB7t+zn16kLS4953T5uO3kEP344l/ysQrJ25vDZuOmMuvD5Sue/9L7zSK2bjKWSsIqUkqLcYpq1a0Lnfh3jjquI7ud34Z3l43n9z3FM2T2B3pedypnX9GTZby7WL7Pz0v2NuaVfa95+oiEv3NOEa085njVLoo3o8l/W8OWLM1k6ZyXeokhPLLoRKHYoYM3CDVyUMZRhHe5lw9+bSclI5skZD+JMceBItpdSGSMEl9Yfxi1dHmDzsm2MnzuK+s3qYnNYsTmtZDapw5BHLsKV5kQ1GT8ZqUs69mpLat1k1Dg6qAILW7bdjJLyVNRje/fzTkI1Rb5PCEm7rm7MpX8WGZ7HMKJmCzhcGiazPLQE5SFASqNCqSK0EOQWXYHInI3I/N6gHK4kNBaNIPh/g8BvlY6KqjxRj0G4hhv88BmfghotyA6ApUviS/H/CoH5lIXAdOP/C0cb6lBHOWqN+lGI1QvXo5iiDYXP7WfJj2XkS3MnL6DwQBGhcmRVAW+A5b+uZvPybXHnT66TxITlL3DlYxfTpE3DUkNVHlpIo1PvdgBc/filCXnrQhV07tuRpDQnzdo1KeVVOfOqXqRkpvDwFS2YPTWNgE/B7zXiyF63Sqwfv9/jj1txY5T3lXGwVGY8pC7Zvnon958xigN78+h8Zke+2P8eo6c/SKfe7Qyxm2IfUpds+mcbI84ew8KZi0FINE2nQYt6jPzkTjqf2RGfu2xNoUCIv2evQNN0+l55OiZLdCxEqKK0YxVAhnYYwg26m+HjryG9fmppo5PNoeFK1bjn+Z1Vfs4ln4GuH/m4erzNJBQykdG0t5HsVFwGP7xjGNUzMV6k5wtkYDkySqkoElIG0PNuQ+achywYiTwwGP3A5ZD8IEY8vOT3YzKodJMeTngV0vdduD69AoQJAgujjx9lqDXqRyHS6qWgxPj1mMwqmU3qlL5etXB9TLIuIQQbl26t9BquVCdDRl7EuytepM0prSIadWxOK+ffdjb1jjE4ehq2rIeegPVQVZX3R37KNcfewZcvG8IHS39eyePnP0N+ViG6pqCFauIrJ8KMiIl7ggFfkO8mGBw0ZouZlic0Y8mPywl4I8M6AW+AyU9+yb6t2QT9Qbau3MGIs8cwcsDYqCSryaQx5I6N3PHE20xfv5ShI/aSlGqMadgiyOiPttCp7VXoWd3Rs3ojc85F5l6PzOpGatJ03l87nlufdnP+0FyGPbqXiX+spVGLxGq0hYA1i+1sXWv51xKm5WG1hZDF7yK17PARC/i+ptq17P6fkXnXIbO6o3tnxx0mi98KM1v6w5UxPgiuAu83iIwvwX6B4bWbTwDX3WBKXOkKEd0/ET5BpGLV0YnaROlRiBPOaI892Y632BdR4qeaVc4Zdmbp6yatG2KxmaPizUIR1G+WGGmaalJ5/ufHmT1pPr9M+Q2b08rAm/rR9ZzOpWN+mZKYdxIKhEoN34ePfEbnMzvy7kMfV4uN8XBBC2ps+qdso9u/PRuz1RTFzGjEhiMNUcAbjEmK9uiE7Zx4ehGKInl4SAvWL3Pgc6sIITmwVyUU8AFe0Ms3x4Q34aLnsTqy6T94K/0vrX5zkNctmP1FHU7tX0Dz4//9z1cIILQEmXslZPxg6IUeVDdrKCxxBxTchzR/HbvixDuF6ARpAHw/IJOfNkpCtV2g7YDQWmTxa5A+EWFuV/W92C9Ger8lZtevtUd1b+iIo9ZTPwqhqirj546iSZuGWB0W7Ek2ktJdPDb1Phq2rF86bsD1Z0TolIKhxZleP42OvRJvkDBbzJwzrC/Pz3mCp74ewSnndik1Yj9/uoB37p8Ytx+oNC5dAcFAiJ8nL2DL8qo5M6wOCw1ahJNrhzFWvGjWPzx33etoIY36zeqW87wlTY/zcUwro448FirWzzds7ufE04uw2iU/fZ7OuqWGQTfGGhQC425pGkUfUAYNPJ/EfsyP947wXF63IGu3hZx9ZoKhqgQyqglTG6gzG0xdOag/hpYFgT9qaDGhMKVCDMh4TWI6+GaGRT98GKWNbpCFyLxbEuqDEJbO4LoRwyu3g3CCcCBS30SIQyrOPyKo9dSPUjQ+rgHvrXqJXRv24PcEaN6haVRiLa1eKuN/GcVz173Org17AejUqy0PTrw9Qp7uUPDeiMlRJYAlcKY6uOzBQXw69kuCFaJAUpdk7cyplO+lhJ/97OvPYOvKHWTvyiEUOHzNNFpIY/60P7DYzOzdkoWUkladPDw6YRvJ6cZ1i/JVxtzYjPXLKq+AaXKsj2BQYLVL5nyRFsFvXnY9wYblDo7vEs9w+wkFBSZzIvETE/O/dZLZMEirjl6aHOvnyYlbQUIoCKYa0XSwIVx3gpqETHsdiseDdwYJt+0DoBkesqU7iKQqNi0rqK3B1AoCs2KMDcXpGgUsPcKGu0J4x9QKvF/FlgSUhUYPQAIdoYrrdqT9IiN5Kxxg7ROXGOxoQ61RP4ohhKBJ60ZRx4vz3fw0cR6bl23j2M7NeXnBU2ghHdWs1mhppRbSOLD7QOy1KYIJy19AUQSfPPlF1Hmrw0JKnSQUkxJTdQgMw6/pGjPf+Qk9WEOEL1XA7wnw3QRDus3h0njm8804k8uubXfqjPt8M1ef3BZ3oYrVrnPaOfnUaxJkw3I7f89LQkrBrs02zGFjHM8oSxn/HICuK6imyPuuyPFSBoVAwMWxHfZgtkZWv0Q7n+Xl66oDG7LgaUMZCQ0jyWiHKpKWERAKmMNNVqmvI3MvjT/W1AxCq0FbE3u9woGw9o59maSHkIFFYePtx5DpMyNSxiALn4q3OKpD+yvUhuAYXPXAowy1Rv0/hj2b93FHt5H4vQH8ngC/fvEHk5/6ktf+epoGzatTH1w1VJNKckZyzGal+s0yqdvE4NQYOnYIHz36GcFACKlLrA4LZww5jeO7teLHj37BG8eol+BwGXRXSoiMBkH27bCU0hCUx/EnuXngkpbs2WqlftMA1z64j+79C1EU6HlePiv+cPHijI1YbBKbXcfnVdi12coDF7dk9xYrm1Zl0vakAjp0c7NmiTOqmciRpNGyfaTHuHGFnR8+S6e4QKXHgEK6988vV8JIqaB2RcP+4xQnv0y3cvo5IqqkM3oTONjPMz8sO1eCYDXoCgAsYD4BYe5grMvSCSlSQMbpGA6tL/dCIZJH3maURdpi024IUxPI/AHp+QwCy8F8HMJxFUJtgLQNguA6omPuFjBVHVP/r6PWqP/H8Oqt71KU5y4Na/g9foK+AG/c+QFjZo6s1lx+r58/Z/5NfnYhnXq3o1m7JlFjrnrsknAIpiy+YnVYuHb05QB8/8HPfPnSTPy+AM5kB+1Pa8PlDw2iXY82BHwBXr/9vUO424ODapLcPm4XZ16cRzAoUE2SryZkMvHZ+pSPEy/7LalUbGLrWjvjbj2Ge17YSa/z80mvG+Sh17eTnK5REslyuHSOae3jijuz+PCZBrzxWGcC3lxy9njQdWMeRQGL3eByGT3RjaKoGAZLY9bHKbz5eGOCfkivF6IwT2X+zGRGvrmj0u7QbeutvP5wY7r0KqoxBsvDAts5iJQxkcccQ8D9IZEGtmTzK38zOobRbVM2l/MKhIhfbSKUdITrtujjjkuQvlkQWhUO6VhBKIjUlxPnf/kPozZR+h9CieZmxTi1rkv+/mlFtebatGwrVzQezgs3vs2EBydxe9cRPDf0dXQ90mpccNvZDBs3hOSMJBRVIa1eCre9cj19rzyd796dzRt3fkjOrlyQ4C7wsOyXVRTkFBldpXYrz88dRUaj9EO+9+rg+pF7OOPCPCw2iTNJx2yW1GsUoGHzyMB/efUgAL9X4f0xDfB7FLassdOirY+KqQmrTdL3kjysdgvuYo3dW4J43WrpXIqq03PgAT5duoLjOuwDkQ6WHrj1u3jt4SYE/QIhBHnZZlb95aJRCz+7KzA+Rnnpn9UhFFRYvdiJyVIT9YuHSVTZ/wsVTYpw3Q7W3hiGNSn831Rih1ssCNeNYXGL66PUihKFEBZE+iRE6ivguAFcdyMy5iCs3Q9qvv8aao36fwwVk6UlMFkS90B0Xefx85+lKM+Nt8hLwBvE7w2wYNqfzPs8snxRCMGgO85h2v73+aZwEp/veZcBN/RFSslHj30eJabh9wT44JHPSl+37NSM1ifH6fI7DFAUybnXHMDmMIyfFoKRV7Tg1RGN2bO1at6cnL1mVi1ysGqRI+5njYDmHZpyYPcBLNZgRDgkFFRY/48jfP0AyGwIzMOqvcSp/fMpqbGXuiDgU/hqQl1CgcqrTIoLTOgaFOaa+OSFevjcgpK9N1RdZTilHtgv57A8pEsf0jM1osJECDNK2quIjO8RqS9CnZlhNaYY9yyDYGpdI0sRQkFYe6EkP4TiugGh/v/RRa416v8hCCHoc3kPzBW6F81WE2cMOS3hebYs3x7BiVICn9tf2qAT69pWu7W01DEYCFGQE7tleteGPbx170f8OnUhoWCItX9tTHht1YWiSAbdkMXAa3NwJoUwW2WEQPT8mams/8cRM6YeCyaL5InrmlOUZ2bTSoMWtzz8PsHPX6TRovVyJv25gi/XrmLamlVcfud+SuLB3hjXMpnhnhd3YTJHeqi6Bn//moS7SCEYx7h3O0vD5jTCEFPfqMfj17bgt1kpLPvdic9dnbJDFZzDEMmPQuaf1LwotR+KxiEPXIyswLUiTI0R1l7g/x4C84guHbWAtRfC1OygriyDG9ALHkPPvQE97170/T3R97VGz+6D7v32oOb8r6I2pv4fw60vX8fWVTvYuW4PJT+MY9o1Yfj4axOeIxQMxWymASoVni4Ps8VEcp2kmElUqUu+evk7vnf9zKTRU6nTIJXcvZVTrFYHiiKQUpLZyM/dz+2ic69ivG6Bu1Bh3oxU9u+y0LCZUbExf2ZKXIOuqEqU2EnQX+bnPHNbU176eiNma1midPcWK1vW2rj3hc2lTwOuFJ3L79iPEPDFW5n0GBA7MSgEtGzvZf0/kaVx097K5MNxDVAUSc/z87lj3G7sTmNdPo/AYiukzYlW1i114vMorPjDybplyQy+uw0n9LWAbzLxqzrKJx81KHoRGdqGkvIEevpnkHsdNauM5IfQemThGHAORXomgbYHLKeCfRC43yY6gQmoTRGpL0UcMqgClCqVhqRvDjL/XgyZvQq7sLYbCh5GR6DYzz2UG/vPoNao/8fgTHHyxqJnWPPHBnas3cUxbRtzfLdWpUZ64deL+ejxKezfnk2zdk24YdyVdOwZWZd7XOcWMUmorA4rZ15VuVp7CYQQXPfU5bx978SoEEzJ47e32MfeLfvpclYntq/ZTcBXM52Pry9+Bofpa9Kc72BzGMbvjx9T+OPHFKRUeOORRjz27jYsNhk2jrGFNJp3aErW9myKCzwReYpmbbz0G5yHzaHzwr1NcCWHqNckVFrS+NacDaUGvQR2p+TSW7OYOz2VIXfFrq1WVVnaoFSCUFCQn2PEuDUE879JJTfLzNOfbiEUFCyem8zJfQvofHoRC75NZd7XqdhdGgOG5NKx+3rwK4AT7OdCYIFR4ifNRhWLkgJ6FpFesRe8U9BtZ6JYeyDr/YMsuC+s9lNVFlYAVmOcUh/0bGJrrQbBN9NIVhI0xgf+Bs9HYWWrWPCViT6HtiELHoXgEkBBWnsjkp9CqGUUGTK4CgLLkEomFDxKzI2i3NwUjzc+o/8HqNUo/R/CnMnzeXn4OxHNQla7hbHfPVxKzlWCJT8tZ9RFz6NrGkF/CLvLxrEnNufZ2Y9htiSeSPv+/Z+ZNGoqObtz4w8SYDKpEcRjB4vTLj6FJ764n+D+81HlutLj917QktWLXaWv23R2c8Vd+9m2zsaH4xrGnc9kMdH6pJZs/GcLAW+Q867LYdhjezCbJUIxkqeL5yYxdngZ6+D09StxJEUbQE2DgE9gd8b+TRUXKlzeqS1q2K4HfIpBq6tHGjqzRadd12K2rrVz4bAcBt+WlQB3ejLY+hrNNabjwXIieKZBKF4C3YyoMx1hboWe1RP0fVVdADCDczjCfh6ozSD4j0ELkLD6UglfT4zNw9IDJf1DpF6MzO4bLoMsGWcyBCoyfgA0ZP7t4P8zfF4hroh3BBSU+uuqHnaUIxGN0lqj/j8CKSWXN7qJ3H35Uedan9yS1/96Jup4zu4DzP74V3L3FdDlzI6cPOAEVPXg4qyFB4q4rNFNCYdvDgZmq4nnf36Cdqe2Qc+5CEKrCPgF309O5/2xDWJ2dZotZjRNi6kpWwLFpJCamQIyl48WrsRaQczD61YYc+MxLJmXDEhe/2EDx3WM9gzjNw6VIS/bxF+zkxECZk1OZ93S6C5FRZXomjHR9Q/v4ZJbsknsz1LNpiNTe5SMr9Cz+oKeADukcBpVJeE6dAA9b7hBVRtx3UqMdykpVvmnOxsi/X2E5WR092Qoeo4oQy2ciNRXkaFNUPQSlXvmMaA2Qsn8pXrvOQqRiFGvTZT+j8Dn9lGQE1sIYNvqXTGPZzSqwxUjLuK2l4fSbWCXgzboYND5HtelRbUFNSrCbDXRrEN0vTwYBjpnVy7bVu9k4jM67iKFkZe1iGvQAaxOC42Oqx/zXAn0kE7u3jxOPK2QUDB6/Xanzunn5SMUo5NTKAfvCKVlhjh7SC79r8il/SnFUYnTEpgtxvEF36YS9Cf6mVaziD20DqkXg+3MqscCoERVp4ikx8KyciWVRTYQLirljbF0DY83g1IXUp5HWE4Or2kTMT1vGYLQNvBMpdoGHRu47q3me/67qDXq/yOwOqxYHbEbNTIb14l4rWkaW1ftYO/WOLwaB4mHJ99FWv1U7Em2KpWVSmB1WDiuS3Nan9ySXoNPZfzcUZxzQ9+Y9xIKhmjWvgn39X6CKa+YmPZWJptW2eMadICrHr2YJ78aSp0GJhS1PAd7NHzu2Oc0DfwehR4D8unYvYh509MIxJAQjdfeHw+DbsgxBC/KbRJWu06v8/JwJmuoqmTjCgffTszA5xFoIaNEs2YfrhVw3lrpOg3YIPnJqGYgYWqMyJwDSfeBbZBRE575s1E6GQ/mLpD2JjiuBMcNBoFWyXzmDrGFn4UK5jYYMfpYEJRtKCYgPIfSEJLHoNjPq+L+/ndQG375H8LksV/y2bjpFbo/rdz33i30udygDF38wz88e+3rBLwBNE2ncasGjPrqgRqjGAgFQ/z13VL2b89m+quzonRCAVIyk2nYsh6KqnBgTx55+/JRzSpaSGf4+Kvpe2VPhrW7h7z9+aVxeKvDwmkXnkL3807ihRvfCqshxU6AlsBsNTF5/XmkWJ5CSo2F3yfz3tiG7Nkam2nPateZsnw1Dlekx+vzCO678Fi2b7DR/HgvAa/g3pd20fQ4P3anTjBglCyWGfUSPm4J5hMh+BexNhNdmli5chTvjZjIrs1WnEkaF1yfzUXDc8jLMjFpfH0WzalDXg60bOfh1LMLaNTCT8+BBTWgT6qA5VSU9A+MtRS9DO4344wVkD4DxZK4qLru+RwKHyf6vu1gOha0zeFuTwugINLeQFhPR0ofMvss0HMoq+ixgKk1os40ZPGr4H6PKGFutQmkvITQc8DcHqHWRUoZt8rrv4ojFlMXQpwNvIJR+PqelDI6gFsOtUb98EDXdT4d+yVfjJ9J0B/EnmRn6NgrGHhTP8Dgjbmp0/0RRl9RBBmN6/DxljdqjNmxBEvnrODxC56N4FO32Mycfkl3PIUe1v21kfzswojKE6vDytjvRtKwZT3G3/AWa//YgD3JzqX3n8eFd57DN2/8yLsPfRLFg14RqknhqgeTGXL7b5Qk8nQdfB6FO885jp2byjcilW0OnXoUMerDbRCOj6smycTn6zPtLUPByObQGD1xKyDRdUGLtj5S65RLFJo7I+wXAJKcnM5sW7mGeqljadwyMjQmJUi1LWrmF2xcup1mdc+NQ/4leOqOYSyatYyAN0DXvoU8+u62qLj/QSF1Aoqtd3g9Erm/HXFLI9V2RjJVKBh0tHawnYVwXodQkqKGSxlAZvcPJ2BLPh+TEaqRHqJj5smIun8ghBmpZSOLngX/z4AKtgsQSfciFCdSdyNzLwdtZzkKABMi7aMIDdj/VRwRoy4MMoUNQD9gF7AYuEJKuSbee2qN+uGFFtJwF3pwpTojDPWEBz9m+ivfRVWh2JNsjJ7+ICee0aHiVIeMlQvW8uFjU9ixZieuVCf7d+QgpYzL3AiG6PT2NbsoznPjLfZhd9lwpTm5+olLWb9oEz99NI9gFQnZ0y/pyiOvfoUgkmVS1+DP2cmMvt4QXrDaNVLSNXL2mkv5W6x2jVPOLMRql/w9L4ncrLJQkmrSGTpyH5feYij8aBrhJKYZlFREnano1Oelm95h7qe/YbGZCQW8HN+lmMff34LDpZd69H6voNjTicx2U9H3dwEZKydiQUtbymfPfI4pOJFe5++jfpNAAhzqCSRNLd1Q0ieVfTZ5N4db/RO1CVZQ6yPqfI1QokMmUstBFjwIgd/Dc5pByQR9T/RUwoVIe6cstl4JpAyCfw7Sv9ioinEMQihHlori30IiRr0m6tS7ApuklFvCF50CXADENeq1OLxQTSrJ6VIKTwIAACAASURBVNHeU/bOnNhlhRLyYlTN1AQ6nH48T896mAfPHM26xZuQWtUGY92iTXiLvKV6oN5iH95iHy8Pn4Cu6wk9UaRlaIaRrGD8FBVOOK2YjAYBUuroXHrLflqf6OHu847F71XweVSEgPnfpsauqZaQlhnEU6RgMkv+mpNM684qdds8grD3RwgLX47/hnmfLyToD5Y+Uaxe7OLVhxoz8s0dpVNZ7RLJCvas/5X6DS4Ez+dEhhUsYB+IyWLmqtu/g+B+EuM2VyHtPXBPCgsox9lAg2uNW9KLkXm3QHAZiRt0jLVq+5HerxDOq6JPywIILCk3ZzC2QTcGk2iKTwgz2AYg4jA4/n9HTTxvNwLK10PtCh+LgBDiJiHEEiHEkuzs7Iqna3EE0KVfp1Kh4/LQQhrHd2912K479fmv2bxsW0IG3Ww14SnwxBSd1jUdJJWWJ5bgp0lLCAZih2jsTp3xX20iKTXEnGlpbFljZ+Kf67h1zG4uuz2XgTcei90Z2xXWNIWXH2jC3ecfy5UnteWZ25syb7oNYelYmkSc8dqsqIasoF/y26wUAhUqWaQOaxZMRyTdB5bOlCnt2A1e8qRHkd6ZEFxBVBw5HoQNIf2I1OdBaRB/nGqck4WPQfCfxOePgC9c0ogRGvFMRS98Dun9Fln0BolXqhi0vbU4dNSEpx7r2x/165VSTgAmgBF+qYHr1qKa6HNFD6aO/4b927JKdU1tTitnXHl6jXOxl8dPE+dF6ajGgsVmJqVuMnn7CtAPsd7d5xHM+7oOZ1yYE6EKJKXBaf7IkBYU5hlf/1V/OelzUR53P7cbhJ8Fsxsy64N9xGtqCfoVtq8PMwgKibtIoXws2lPoIaNBIKJbFIwmo6BfRHDT2Bw6AW8BQtgR6RORwbVGWZ+pOcLcHs0zlyVfj2Hj8nQyGwU5/dx8rHZZefhF+pAkoSjJkDETmXdrOFlbfjO0g/0S9NzbIBBf4LlqqKA2RIa2Iw8MDsvMeZHCkYC4htn4JwQi7c3/F7S4RwI1YdR3AeULixsD8Z6xavEvwmq38tqfT/PVy9/x69SF2Fw2Lrjt7ISpAQ4HVLNKev1U0uql0m1gFwbdMYBXbnmX3776Cy10aB2orz7UgMyG0O6kA6WycV+9m8GH4xpQ3hcJ+BT+npfEtnUWmrbSyNrrwFOUSJci2Ow6XfsJUFsAIIMrmTBvLUkphQhgyxobT99yDPt3Wqnf1B+hsgRGMrbvoL+RMmBQxpqPB7NRZeIpLuKBni+xY2Nj/F4Fs1ny4j1NGDpyL4Nvq+xpV4P8q9HNJxvGMv0DZNGLhiYqmvEk4LgKil+MLftWLaig7UPmnE/EJig9VKlx6roPoaQaCVfFVfnYWiSMmkiUmjASpX2B3RiJ0iFSytXx3lObKP3/hY+e+Jwvnv86ylsXQtD+9DaM/XYkdlcZd3ZeVgF393iEvKwCAt4AIGIaeEVVSMlMIm9/QcxQsMmscnz349izYRVJqUH2brdE1bT3GZTL+dfn8P7Yhqxe7Azzpytoocp+F0a1jM2h0/1sNyMmP41i7YzUc8Mt7mUMmFoI8nLM3NirDTc/uZOzBudHedkSB0rqSwhbH+O1XoAsepHJY+dTXKhzSr9C8nNMzPwwg1WLXJx6dgEPvLojqvQyxicA1jNQ0l435pUBkMUgUpB5N4fj7Yn8/pVyXC8hSmvCIfw6mOA85ZfWDiVjevXeU4sjkyiVUoaEELcDP2KUNH5QmUGvxf8/XP7QIBZ//w871+3GW+zD4rCgKAoPfXQ7p110StT4tLopfLD2Ff76bik71u4is0kdJj35BXs2RvKT6JpO3r44UmkYvC5tuv5fe+cdHkXV/fHPndmeThJq6E1pIiKiomBDVAQBQexixZ9dUXixoCh2bPgqNnixISKgICKCKGIBkd6bSA0lCZC2fe7vj1kCm91NIYEA3s/z5IHdmblz7iZ75syZc7+nGSvnrSN7V+Sfervz87jtiUwGXtScglwdKQVmut4gVpRptQdJTLFwypkJdL2hOR1734YWEpqShV+DDL/46BZITBF88EsmqdUjHTqAIFAUMUvpM9MYwa107qmTVsuPwyUxDOh4SS4fjajFtx+nkbnFRkZjbymljQHw/oQ08hFavJnzF2aViPQvo8wO3doeUe0Ts3ZcOMHIBpmPzB0eysWXFxsicdgRHKcoC5Wi0iil/A74rjLGUpx8OFxm2uevmctYt3Aj6XXT6Ny3Y1h0XhzdonNOzzM5p6dZ4lanaS3uO3tomfyQ0AS1G9Vg0Jj/w+fxM/HVqVH3u+7B3cydmozfZzauOGyEKHtLmrR20+v2vWxel8TUMRaqZaRw9tWHldIFtxHtwaDNLkir2wJ8v3N47r0gV2PbRgfptX2kJgXNs3p/BGM3ECS9toHdaU5Y08Dhktz2RCazJ1bjkaua0O/ePVzUZx+pNf1YYn6TtdCdQ7H0hp4OgVgVTzpmxYzLfOia9Ly5iOdgo4lQqkT6V8Y6aQloEHcbwqYeih4tlPSu4pigaRodLjudM7u1ZcmPK/ho6HiEgD3bslj12zqc8Q6uurcbV91/eVQNmq1rd5T5Dv+UDk1587fn2LpmO6MfHhdzv5r1fMz8IqVEmYFDCPZnWeh0xQE+frUmPo+fWR/PpdW5p3DhdeeZe9jaI91TKK5PHgh4+eb9Dcyb1pTsXdC8bSFxSQHmTKqGxSbx+wTtL/yYoRO7YguuDuWjKXLoYWP5Bae0K2TxLwmMe6kWE96uzsSVq8AS48MRyUjvH8jCz0EEwd4TtDiwtoNA8YuQA5w9EbaOSP9qhKWRWToYpQbdHDsBZCx1ThtR0zLCgbCXvaGLovwop644ZhiGwfC+I1n0wzI8BeHlcwf25jL2yQlsXLaFwf+7N+JYq82CEKXrngghqNmwOpPemM7YJ8bHXHmqW3T25TSgSet9/DItWCbHvj/bwnvP1Gb3NrMs1FPg5Zv/fl/k1HFcAvn/Jej7B103I3JPoWD5H/G8/3Q6B+8A9u60huYhijRkFs0xeHPg+9w8NJV5E2rR4aJsMhpHLjLSNMjdZ9pqdwbp+38F2OI7hapbDq82Cakhak7IfezQ2/4VHNJF95v7CIspmOW4FLS65gVArw6Wi2M7dIC4WyD/HcIvDFbzghF3Gxx4EmQ24cv9m4C1xJSwooIop6446uzZlsWk17/lz++WsPPvXRhRatABvIVefvnyd2555hpq1A/vKdn8zCboVkup0r42p5UL+p/Lc9e8VmIZpW7VScgYwiUNHmD8mwZ+r1a0ojSWpkzAJ/juk7Sw99z5hxyaEDbGvdUbW/B/dOm1j4BfMOOzVL7+MC1sPBllUZPPqzFn/C/88pUVaaSxYJaT4R9vDmvGYRiQt19n0yoHKel++t+/m5635kJgFyT/18zLe2dBYCtYGoLeEApejziXOb+Ddlsg6Q1TfXHfDeCZaW7zC6TnR2Tik2iuvlE/QxF3BzK4C9yTQFjNEkZHd0TSs+Zyf+tkZN7L4J1tnsfZAxH/8Emnx3K8oZy64qiybd0O7j3rP/jcvjI1ybDYLGxa9k+EU6/duCZd+p/LLxP/CFXEmDromibQdB2LVUdKyT1v3krWjpzYjkOAzWGj36ArSanTHqdjPMM+HsoXr+WyeF4CRhCCgVhr8sLHtDmsdO53qEP9inlrGP/CDxhGLca+WMKinxgYQYkv6Ac0lv2ewJjna3Hb45lYbBJdB02zU6Ph+Xy//SfCNFqkH/Y/BNam4F9ldjyydAPPjDKcNQD+xRBYDcE9HFqAFHL8ucMxbBcgjM1IzywzfeLsgbA0QQgdkfQ0MuFBCGwBS92w5fpCTzcXQCmOKcqpK44q7z36Ce48D2UtnTWCRoRDP8igj+6mxVlN+ea/3+Mp8NKp91lcN7Q3efvyycvJp1Gb+tgcNr778EdEFF13oQlanN2MuKQ4Jrz0DeNf+JqM5rW5dsiDLP1tNH5v7MUy6XVTOZCVSzBgEPQHccRZqF4nQM/rP8PIz0a4rmfiyKkYRuWtq/tmTDo/TkrjrhFpdO29CMgH/49E13TJP1SJYuyF/LcgitBWJAZIL3h/I/qKUi9knYss0pLRkAVjkQlD0OKuBzBrzW3JRzBDxdFA6akrjirL564us0O32Cw0aFmXxqc1iNgmpeT3rxfy84TfsFgtXHb7hdz0dD8SUxOo06QWp3RoitVuZcW81eTuWYfdEVmFYrVb8Xv8LJ69HL8vQDAQZMuqbbwx8D3aXtgKiy16jONMcDJuwyjufn0A1eulkZxuoXP3bN6YugyXYxXkv43M7svebeWRv5AIYX4uQkgsVgOrLfJzKsgT7Fi3FjiAWZFS1kYYbjBKaDFYhAPh6AolCmLJ0LkP/uuFvBeRwewSjlFUFcqpK44qcYmxyxZtDitCCHSrhsVmocNlp/P8jMej7vvB4E94+Za3Wf7LGjYt+4fPR0zmng5D8IQ0VoKBIGMH30f1+H70vPZNPvtrBc9+8jepNQV2lx2bw0qv+7qxZc32iLx8wBegduOa3P3azTjjHUWpG4vNgt1l58kvH+bDwZ/y3iPjyNy0m/17A/w8LZ5nbmtIMAimsNVO2nWxx7gwyGI/piNv2aGAhi3cnHv5AYaN2Ry1ht1iNehyVVmcczTsYDmj5F2cV5pywXE3A7F/V5HoZqNrxXGHSr8ojiq97r+cj5+ZGCZwZbVbaHZGY3rc042O3c/A5/Fhd9pi1q1n7czhm7e/D3vw6fP4ydqezayP53LlwK78OnE8/e+ejcN5KJI9/bw8nhm3gXUbXuTsHu3ZuGQz00ZH6pwE/EG2rt3B/70xgO4Du7Jo1nIWzVpGcnoiF9/YGb/Hz9O9Xg47v7dQZ91SFwt/TKRj11zATe879/DDpy7y9hcckhYWRFV7lFJj8xon787eQI0ML1s3JJJW22Dn5vA4q8+de2h4annbtx3EDymjYG9nonYM0lIRic+aFzF7J2T8vWbaBh+l1o8KgandojjeUJG64qjS5+HuXHT9eVjtVuKSXNgcVtpd3IYXf3iSC6/thCvBSXJ6UokLkdbM34DFGhl/eAq8LJxh5pGF5zMslvDUhNUGdRu7aXu+hfSMVBq2rhe1esbmsNIipFKpaRpnXtqWga/eTP/BvUirXY0lc1ai6ZFfFU+BzoLZB/PWOik1azN66atcObArGc1q0arTKTw29h5cCdHnVpin8+7TZ7A/9xwe7NGUzH8i53jWJdH7zpaOA5xXoelp4LgCs248fHuuux/Lfl7Fgaxcc+7xdyCq/2a2mytNt0UaYO98hLYpjiYqUlccVXRd56H37uLmZ/qxdc0OajasTs0G1aPum7Uzh/HPT2bh90tJqZFE30E96NTrLFKqJ0bNy2u6Rnpdc4l+eu28MDXGgwSDAl03c901G1Tn3Ks68PvUhXgLQxU0mpme6T7wAmThZKR3lhnBuq5FWFsCkJASh4ii4W6xGiQVdT2yIlzXk5qUwj1v3hq2X/2WdbnnzCFR7JfoYg8bV7WhVv11bFwe+XX8aEQtRnz2d1hpY+k4wXUjIuFBAETiMKSRBb6FIGxI6eWvuTVZMvdbzrzwcxZ8YSHPfRW9Bz2G0BIhaTgy++qQ4uLhF8qQqiISkfKWEuE6TlFOXXFMqFYzhWo1U2Ju37d7PwNPf5T8fQUEA0Ey/97NSzeOYuvQ7fQf0ovk6kl4C71h1SVWm4Ur774UAGHriNc9LWIVptVm4Pc2Ydq7M0mukcxDHwykQau6TH3nB9z5Hs7o2obbX+xHsn4XMm9TSINFQ7qnFtVon3VFO/QokbquQ0YTycTRdajZvC/n9GmIFSjILWT2p7+wcfFmGrWpx8U3dsZiC6+xr9PIy6uTNuKIM7DY/mHk5CDzZyXy0j31D6uXh5UL4nnihkbc9sROGjT3YnFkYHXUBv8iojdhTgRHN4SrD6bWHggtzlRqDGyF4Hbeunc6vW+ZSutBPhwuSTAIft9Yls0M0rbbUISlCaR+hcx706yo0WuB8xoEQRB2sF8UtYWd4vhANZ5WHBd8MPhTJr85PSI9YnfamJD5AXk5+TzV8yV2btqFputouuCRD+7mvD4dAQj6ssnffCFOl7soYvcUaiyb34QRdyQBoFl0rHYLr855moat6hWdwygYD3kvEKnb4jD7ZmpxrF+0iSe6v4Cn0IsQAiNokFIjjv178vB5DWwOK3GJLp744iGe7v0K7gIv3kIvdpcdu8tGq3Ob8+eMpUXze2/OWuo19aIdtpDVXSh476nazPj80AInTRMIXUPXNW55tj99H+mBlG7kvntCWjLRqmE0EHZEyscRfTsLDhTwxdNXcO39mTiKXQC9bh17nS8Q1pZFFwTF8cUxazxdXpRTVxTn7jMeY+OSzRHvxyW5GDF9KC3PaQ7A9g2ZFOYW0qhN/Yg8uxHYTc6m53BY/sAwXPy9sTNPXfM37vzw+nNngoNP/n6HpFQz2jRybgbfH5FGiXhE8iiE/VwAgsEgaxdsxOfxMX/aIqaN/iFMhkDTNeKT48jfXxDWnUlogtM6tyR//wF2bNhF9Qwvo6avwu6MdMgblju5t1uz0HGS5m29aBbodse9XHbbpUX7ycA2ZFY3okfrISwt0NK+Dntr7/adeLdfSu0GkTXpUoIQDjMaT3wezXlJ7LEVVcKx6lGqUFSYGvXT2LR0c4S2i98XoFqtQwtbMprGXqmpWWqQ1nxU0euxtzwe4dAB3Hke7jlzMOPWj0K36CASY4xomA0lQui6XnRxeeH6NyN0ZYygQW525INNaUiWz13J9K1rWLMokX17DKzFn1uGsIWkdJu2KeTpsZtxJRhICUbwQTwH3sGRZGqu418YWppfglMPrEHKIIW5HhbNWk58/DZOa/sKRkb0tnVmSaXHzKUfeARpmYSwNo09vuK4RFW/KI4qB7JyKcgtLHW/voN6YnOG90819dCbHHGrvVhiXgD79+TyxzTzblG4rieyRluASAJrm6jHy3KuHNUtBkL4aHlmFp2uyEHTo6VN7Gz9uy12Z5AXJ2wirVYAV7xBXIJBQnIQPf8+ZHB3yLwUSq1QwcHcifO5pvadvHbHO2TUHI7gAHqZQjm/KeylOOFQTl1xVFi/aBO3t3qI/hl3cXX12xjc9VmyM/fF3L/lOc156P27iE+Ow+6yoVt1WnU6hacnP1qu80opkb7FyIIxXNA31YzEo+B1e9m8YisAwt4R4u9m19Z4pn9SmzlTalBYWB1R7SOEiP4VOb/fOViLLTQSQpBcPRGrvdj7miS9to9lv8VHUZk8GLK78Bt1GfWon3O65Ybl2g+NL5HukDa8vROm0mIsHOzddxWvDHgHr9tH7fo5uOKji6FFz8AGwVBdKU9ElFNXVDr7du9n0IXPsGW1uXoz4Auw7OeVPNJlGIYRe5l7+66nUfeU2hhBid1hY/Xv65n6zswyn1dKH3LfAPMnbyRX9p9AjYzoC3eccQ7qHJbKGft8And0OYX3nq7JW4Prcl3bBiz/NXqaAuDyOy4iITUBm8N8KuuIs5NQLY4R04fSsE19HHF2NIv59ZIG7PzHzrBbGjDqP3UOG8UKrpvB2R+R9DyD+59G7r4gCSkB9Cj66ELzg5GN9HyPzLnRTA2JBMy7jIMXEidgB3tnfvmuLTL0eVvtEhnjo4+ufeYE23kx5684flFOXVHpzPjoR4L+8KgwGDDI2bWP5XNXxzzu2X6vsX7R3/i9fgrz3Pg8Pr54cQq/f7OwTOeVBR+Db3GoLNGPzZ7Pu7PWkpAiwzIVmq7hTHDSqVcHAJbNXcXXb83A5/HjdQdx5/tx53sY1utlfMVSOFJK3n1oLPd3HEphbiEIgd1po++gHny6+R2andGYt+e/wP3v3oFW5C0FIPAU6syeWI0Ny0OpHi0NkTAILWk4uQWdWL/wH6QhWfFHfFQHLITLbPJ8YLCprGhsM/PfIg5SPoC0nxAp7yPSZ6GljMJTECha2bp+qTNGRO4E69mEp59soFdHOHuX6XNXHF8op66odLatz4yqZS4Nya5/ooteZe3IZvUf6w8trw/hKfAycWT0dnQRuL+ieFmiI87g3VmbaN/1VFOq16LR7qLWjPpjBDaHmfqYOfYnvO7IqDwYCPL7N3+Gvff7Nwv57sMf8Xn8eAq8+Nw+vG4fM8f+hCPObMYshCAnc39UxUa/T7BgdhLgQCSNKNKZ8fsCRSHz5jVO5n2bjLvg0JXIU6hR6G5oapOH+pmGRgSZB/7VaJY6CPtZCL0mAB0ub4c1NMeAX+Pl++rjKRT4vAfHtYFeF5JHI5JeMFeS6k0h7i5E6uSSG2QojltU9Yui0ml1TnN+nTQ/oruRNCRN2zWMekxeTj4Wmx714eb+vbllPHN0vfb02gGen3YnQWk6u+KlkD6vP2oU6ynw8uINo1g8azn3v3MHFquFaaNnYnfkI9BwFxxKfOfl5LNxyWaatmsEwG9TFoSVNR5ECEnm1gRE6ocIa7Oi96vVkAwYkkv12rvZtMrBh8/VYuFPCVx+fQ66RfLT12l0uOJsOp6/xWxGEYYXvPMg/o6wd5u3b8xF13dizue/4inw8uePiTzYoxUvTdyGzZ4HSAhuh5wrodpnaM7LY32wihMI5dQVlc5FN5zP5y9MNvPpocjb7rRx2gWtosrqAmQ0r40WbSm+zcJZl7cr03n353XBqX2M3RHuoX2BNOx6HSwxGmdccM25LPh2UcRFCMxofc7nv5KQEs/tzzXn4Rcnk5hiVvMs+jmBkQ/VJW+/BaGJItGyrWt3sHHpP1HPFQxozP7SRcP2a+g3yHTqMrAFsq+m1+1uNM1Hh4tzuXrgXh68simD+zUGzNr68/vXp/iFy+8TzPs2hQU/6aRkjOWKOy4moVo8i35Yjs1p466RN9O57zn8+Pk8NE1w3YO7SExZHxonCPgx/NsgZxCW9E/K9Dkrjm/U4iPFUWH/3gOMGzaBX6f8ic1h5Yo7LqbvoB5YbbGV/WZ/Opc3Br6Pz+1DSlP/PD7ZxXtLXyWlRulNGIZe8SQ33T+VjMZeXPEGnkJBMCAYPfxCHv30nYj9s3ZkM+WtGaz9cwNZO3LI3plTpAlTHEecjSnrVqJph1Iffh9sWuXkgSua4Upw8uXuDwn4Aswa9zOjHxlHMEbbPgCrw8pLM5+k9XmnYuTcDr5fOXx1qGHAij/ieKxvE4QQJKUn8vmWd9Dz+kBgIxDE5xE80rsxW9c78RRq6KEHswiB1W5FEwIpJc98/RinX9gaAN+Oc7HokSmwgF+g1/wT3ZpU6uesqDrUilLFCcfqP9bx1WvfsmdrFmdc0obeD15BUlqsxUHhdLP3RwYDdLg4lxbtC9i708ZPU5IpyLPyve+LsDuBLau3cf85j+Pz+An4AugWDd2i4/cFotagCw2mblqNzR6eHvIUajzW91Tadr2an8b/SnbmPoygUaY69o7dz+DZqUMwdrUk2spQw4Crmp5BnaZ1ePLLh8loVhsZ3IPcfy/41zBtXDU+GJ6G113yozFnvIMJmR+wfd1OUm3dSU6LLG30+wTLVr5Lh8svLNXuaEgpzY5LwmGKgimOCmpFqeKEo8XZzXlqYvMjOtbhslNwIMj8H5KY/8OhiNPuskX0LP3vA2Nx57mLcunBgEEwYOBMcODOiyyDrNNIi3DoAJpupf+QS3hxwHcxo/xY7NmaFVKfjH4BEMLG2HWjSM84pAUj9OqI1C+RwZ3Mnf4aXveWUs8jhOCv75cybfQPnHNREpddlx22otUwYNtGO6t+302HI0irS99C5IEhENwNSKTtLETyq2H9ShXHjgpVvwgh+gohVgkhDCFEiVcPheJoc8UdF2Nzhq+/tzmsXHpLlwinvmLemqgPR915HrPGPNTjVAjzecA9I08DHBH72+ww/aPMcjt0i02n7YWtQqJcMZy687Iwhx62Ta+NKym1TOeSUuLz+Fn/1yY+ebUmWbusuPPN+XncAne+xltDGsXsDVvi2IFtyJzbIbgNs7mGH3zzkTm3lLmNoaJyqWikvhLoDbxXCbYoFBXi5mf7s31DJn/NXGr2I/UFOK1LS+585caIfR1xdvKjNcxw2hg1/wU+f34yGxZton6LDK4d2odm7VKRWdPA8HPoYaUDHJexfUP52s3pFh1Xgot+j/ZEel4metWOBrazSxznyoFdWfbzqqgPeA8n4A+wf88BHPEOsncUcmeXU+jScz+nti8gc7ONvZk2mrT2ckG/eiWOEw1Z+BlQ/HMMQHArBFbElFlQHD0q5NSllGuAiChIoTgSDMPgj6l/8fOXv2N32uh264W0OveUMh9vs1t5Zspj7Ny0i61rdpDRvHZMAbDud3VlypvT8boPRdhmVH8BDVrWZehnD0QelDoFmf8GeOeCcJmNKFw30vzMt9i9ZW+JeXSbw0r9Fhnk7Sug/aWncd3QPqTWSsE4oBPqeRd+gHAhtENiYlJKU9s8uBOsLRCWRnS4vB097+nG5Le+w2LVQZoOXNM0vG5fSGpAEAwa/O+pL4oe3Po8Gj9MqMa6JS5e+mojdgc4XFY0dx8M+iASh5X9Ox38h+hKkRoEdyinXgVUyoNSIcTPwCApZcynn0KIO4E7AerVq3fGli2l5wIV/x4Mw+Dp3q+wZM4KPPmmZrnNaeOax3py41N9K/18fp+fF65/kwXTFxdF9W0vaMlTEx/B7ixJUyWSf1Zt476O/wmLmDVdQ0qJpgkatq7Pwx8MLKphPxzpW4Tcd2uxBUWAcCLS/0BoLmQwG7nvRtOhI0AGwH4hInkkQljYuz2bFfPWkJiawGmdG7B06gB+nZbH7u0ay+fH4/eEZ1mFENjjbLw3eyk1MnyEy9s4EckvIRzdyjR3I38M5L9BpBa9HZE2HWEpf/SviE2lVL8IIWYDNaNselxK+U1on58pxakfjqp+URRn4fdLGN53ZEQqweqwMm79KNIzypY/Li+Zm3ebUX2zqScwnAAAEBFJREFUWtRpElvWtzQ2LtnMB4M/Zc2CDSSnJ9J/yFVcfOP55sPXuMhc/OEYua9C4ThAgtBBhtrF2buY23NuBd98wtMcDoh/AC3+tvCx8kZCwVjAxwPdm7B2cRzFsTmtvDKzP82bPInAHbEd29lo1caVad7SyENmXQZGzmH2OcDRFS351TKNoSg7lVL9IqW8uPJMUiii8/s3C6PmhnVdY9Gs5XQbcMFROW+thjXKJe2btTOHLau2UatRDWo3PhTrNDm9IS/98GTkAWUI+rXEQUjX1eD9BYkd7B1Brw2YThPfAiLz1h5wfw7FnDrubzAfWJpplmjouk5iNZupQBktpit+11ACQksIpaVGgffHUFrqBoTrhjKPoahcVEmj4rjAlehCt2gRC3aEJnDGlxzpHm0y/97Nrs17mDFmDr9OWYAtlK5pc/6pPPXVoFIj8bIgLA0w/CvMtnp5w5FYkK7rwXUTMXXTS3G+Xa7ax/a/7RHO3e6yUatZF8iOJkvsAEf38tmupyOShgPDy3Wc4uhQ0ZLGXkKI7cDZwHQhRNl1UhWKw+h6S5cITRYTwVlXlE0moLIpzHMzuOtwbm/9MI93f56fxv+K3+On4EAhPreP5XNX8/Z9H1XKuaR3Hhx4HIwszAePbij8FArGmI2fI7CAPUq7OWdPDt4e9Lw1i7pNPDhcZnWN1WbB7rLzn08fQLc4EEmvYJZphj534QJrM4TrmkqZk6JqUCtKFccNM8b8yNv3jsFiMyNIIQTPTh1C6/NOrRJ7nu03kj+m/YXfG725BJhSBlNzP45xQSo7RnZf8C+LssUBKe/D/oHmA1J8gBO0JETqFIQe/qxBGoXInBsg+DdID36/g9++S2HJn5eRXq8B3QZcQPV66UjpB89MpPt7cyWoXgPhvAzsFyNEbCkHRdWiZAIUJxz5+wtYMmclNoeV0y9qjc1eNQ7Gne+mT9qtpiRuCegWnSk5Y3HGF2+HVz6MPWeDkR1liwORbt4Ay8LxENgMtjMRzt4ILT7qWFIa4PsN/CtArwOOS82G0kXbPcjs6yDwN1CIGalbEMlvIBxHJhOgODYomQDFCUd8chzn9T6rqs3Ane8BrfRa7TpNa1bYoQNgaQm+XyLfF1azmYawIhIeLtNQQmhgP8/8iYIsnBASBTtYhhgAAsgDj4J9vorUT3BUkwyFIgopNZJLFBLTdA27y86Do++qlPOJhIeIlCFwQvz9le9k3d8SWVcOYIA/dmcqxYmBcuoKRRSEEDz03l3YXYd0YHSrjtVupVn7xlx224W8u+ilCuX7A/5AkT6KsLZEpH4KtrNAxIPeCJE0Ai3u5kqZTxgi1p2FBFG+hVeK4w+VflEoYtDhstN587fnmPjqVHZsyKT1+S3o81B3UmulVGjc379ZyLsP/4/d/+zBleSi36Ae9B/SC83aBlHt6DeqEHHXIQ8sK1YSKUBLA8uRKWQqjh/Ug1KF4hiyZM4KnuzxYpiqo91lp8/D3RkwvP8xsUFKicx9FtwTzRWsCFMHvdonCEuTY2KD4sgoy4NSlX5RKI4h456aECHT6y30Mvn1b/FF6c9aUQwjWp9UgZb0lKnNkvgUIvl1RPovyqGfJCinrlAcQ7ZvyIz6vpSSA2VusF0yhmEw/sUp9E4bwKWWaxhw6gMsnLk0Yj9hqWeWRtq7qIqXkwjl1BWKY0iDlnWjvq/rOsnVK6cN3NgnxvPZc5PIy8kHYPu6nTzT5xVW/rqmUsZXHN8op65QHEMGPHctdld4dyaHy851j/cusSl3WfG6vUx5awbewnBxNG+hj3HDvqzw+IrjH+XUFYpjSMtzmjPi26E0adcQi81Cet1U7nrtZvo92jNi341LN/Pqrf/l0Yue4YsXp5C/v6DU8XN27SdWf4vlv6ymq96Pa+vdxcz//VShebgLPKyev57MzbsrNI6i8lHVLwrFcci8yQt46aa38Hv8GIbE5rSRmBrP6MWvlLgoyufx0Sf91lJb3Nlddu55awCX3XpRuW2b/Oa3jHn8C3SLRsAfpNkZjXhmymMkpiaUeyxF+VDVLwpFJeHz+Jj6zkwe6TKMJ3u8yJ8zlhy1cwUDQV6/czTeQh9GqEWez+1j/55cJrz8TYnH2hw2rn7kSuyukhcReQu9/O/JCeW2beH3Sxjz+Bd4C70U5rrxuX2sXbCBZ65WDTGOF9TiI4WiFPw+Pw+e9yRb1+woylUv/WklvR86OrXl29fvjCokFvAF+P2bhdz5cmQj7cO5aVg/EqvF88WLX3MgK5dg0IjaDCMncx/BQBDdEk1XPToTR06LyNcH/EHWLtjAnm1ZVK+bVuaxFEcHFakrFKXw84Tf2bZ2R5gz8xR4mfjKVLIz9x3RmFJKVs9fz2fPTeLrt2ewf++Bom1xSS6C/mDU4xKqxRMMBPn67Rnc3uohbmp6Lx8N/ZyCA4fy7UIIet1/BRN2fsD3vgkx2/RVq5VSLocO5oUgGhabpdJKMhUVQzl1haIU5n+7KGqO2mqzsHJe+csEDcNgxLVvMPiS4Yx7egIfDP6UGxvew6JZpp56Wp1Ump/ZOMLhOuLs9HnwCkZc9wYfDvmMLau3k7lpN5Ne/5b7zn4cn8cX7XTc9vx1ERU3dpedAc+V/y6jfbe2WGyRN/jSkNRvkVHu8RSVj3LqCkUpJFdPQtOjf1USqkXXNI+Gz+vHMAzmTVrAgunmhUIaEp/bh6fQy3PXvI7fZ64qfWriIzRoWRdHnJ24JCc2h5Ue93SjXosMFkxfHHbX4Pf62bsti7lf/hH1vOf16cijY+6hZsPqCE2QXjeN+9+5nW4Dyq+dfs2jPUlIicN6mGO3u+zcNfImbA5bCUcqjhUqp65QlEL3Oy9m5pg5eN2HImEhwBHv4LQLWpZ6/ILvFvPf+8ew+5892OPsJFdPihr5G4bBqt/W0faCVqTUSGb0klfYtOwfcjL30aRdI1KqJ/H9mDlFqpGH4ynwsmzuKi65qXNUGzr3O4fO/c4px6yjk1IjmfeWjWTS69P46/tlpGVUo+8jPTitS+mfg+LYoJy6QlEKDVvX56EPBvLGwPfRNIE0JImpCYz4bii6XnJOeuVva3m278iiC4I7z4O3hHJDUazIvPFpDWh8WoOi16m1U9C0yLsGq91KzYbVyzGrIyelehK3v3ADt79wwzE5n6J8KKeuUJSBi647j069OrB2wUacCQ6atmsU4YCj8cnwiWERPlBUplgcTdNoeW7J0rftLmlDXLILT4EnbBzdYnDpLdGjdMW/C5VTV/xrkUYe0r8OaeSXaX+7085pXVrS7IzGZXLoYOquREPXNWwOK7rF7KDkiLPz1FePlNrAWtd1Rv40hCZtfFjtBnanQfUMHyM+3Uxq/AtlsklxcqMidcW/DimDyNznQnriVpABpKs/IuE/Zn/PSqRx2wbs3ZZF8YXbFruVF75/nJXz1hKfEkfnfmeTWK1sKzJr1PiNUd9tJnuXH59Xo2Y9nykN4JmFDGxGWBpW6hwUJxbKqSv+dcj8UeD+CvCBDKVGCicgtTREfOX0HD3ITcP6sXj2irBqFbvLTt9BV9K606m07nQE7fB8CwA3qTWLvS8s4F8Jyqn/q1HpF8W/BulbhJHVHQreAYo/rPRAwdhKP2eT0xvy8uynaHF2M2wOK+l1U7nz5Ru4aVi/Ix/U0gCIpugoQS/u6RX/NioUqQshXgGuBHzAJmCAlHJ/ZRimUFQmMrARmXMr4C5hpwOxt1WAFh2b8eZvIyptPOHqjywcB/LwTkk6aDXAWqLWk+JfQEUj9VlAKyllG2A98J+Km6RQVD6y4EPM2KMELEeQCqkChF4bkfIh6BmAHbCC9Qyzx2gZH+AqTl4qFKlLKX847OV84OqKmaNQHCX8G4DoeiomDkTiE8fKmgojbGdC2o9g7AZhR2gpVW2S4jihMnPqtwIzYm0UQtwphPhLCPHX3r17K/G0CkUZsLYmZgxj64JInYCwtTumJlUUIQRCr6kcuiKMUp26EGK2EGJllJ+eh+3zOBAAPos1jpTyfSlleyll+/T09MqxXqEoIyLuNhDFNcYd4Lwardr7COuJkXpRKEqj1PSLlPLikrYLIW4GugMXyapoo6RQlAFhqQvVvkDmPQ++xaDFg+smRNydVW2aQlGpVLT6pRswGOgspSysHJMUiqODsDZHVBtX1WYoFEeViubU3wYSgFlCiKVCiNGVYJNCoVAojpCKVr80qSxDFAqFQlFx1IpShUKhOIlQTl2hUChOIpRTVygUipMI5dQVCoXiJEJURWm5EGIvsOWYnzg6aUBWVRtRCah5HD+cDHMANY/jjTQgTkpZ4urNKnHqxxNCiL+klCe8tJ2ax/HDyTAHUPM43ijrPFT6RaFQKE4ilFNXKBSKkwjl1OH9qjagklDzOH44GeYAah7HG2Wax78+p65QKBQnEypSVygUipMI5dQVCoXiJEI5dUAI8awQYnlIafIHIUTtqrbpSBBCvCKEWBuayxQhRHJV21RehBB9hRCrhBCGEOKEK0MTQnQTQqwTQmwUQgypanuOBCHEGCHEHiHEyqq2pSIIIeoKIX4SQqwJ/U09UNU2HQlCCIcQ4k8hxLLQPJ4pcX+VUwchRKKUMjf0//uBFlLKgVVsVrkRQnQF5kgpA0KIlwCklIOr2KxyIYQ4FTCA94BBUsq/qtikMiOE0DEbsF8CbAcWAtdKKVdXqWHlRAhxPpAPfCylbFXV9hwpQohaQC0p5WIhRAKwCLjqBPx9CMxFR/lCCCvwK/CAlHJ+tP1VpA4cdOgh4oAT8konpfxBShkIvZwPZFSlPUeClHKNlHJdVdtxhHQANkop/5ZS+oAvgJ6lHHPcIaX8BcipajsqipQyU0q5OPT/PGANUKdqrSo/0iQ/9NIa+onpo5RTDyGEGCGE2AZcDzxV1fZUAiU2AlccFeoA2w57vZ0T0ImcjAghGgCnAwuq1pIjQwihCyGWAnuAWVLKmPP41zj10hpoSykfl1LWxWyefW/VWhubymoEXpWUZQ4nKCLKeyfkXd/JhBAiHpgEPFjsrvyEQUoZlFK2xbz77iCEiJkWq1DnoxOJ0hpoH8bnwHRg2FE054g5GRqBl+N3caKxHah72OsMYGcV2aIAQjnoScBnUsrJVW1PRZFS7hdC/Ax0A6I+yP7XROolIYRoetjLHsDaqrKlIhzWCLyHagReJSwEmgohGgohbEB/YGoV2/SvJfSA8SNgjZTytaq250gRQqQfrGQTQjiBiynBR6nqF0AIMQlojll1sQUYKKXcUbVWlR8hxEbADmSH3pp/olXxCCF6AaOAdGA/sFRKeWnVWlV2hBCXA28AOjBGSjmiik0qN0KI8UAXTKnX3cAwKeVHVWrUESCE6ATMA1ZgfrcBhkopv6s6q8qPEKINMA7zb0oDvpRSDo+5v3LqCoVCcfKg0i8KhUJxEqGcukKhUJxEKKeuUCgUJxHKqSsUCsVJhHLqCoVCcRKhnLpCoVCcRCinrlAoFCcR/w96yVe5uAnNDgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], c=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# From: https://scikit-learn.org/stable/auto_examples/linear_model/plot_iris_logistic.html#sphx-glr-auto-examples-linear-model-plot-iris-logistic-py\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "logreg = LogisticRegression(solver='lbfgs')\n",
    "\n",
    "# Create an instance of Logistic Regression Classifier and fit the data.\n",
    "logreg.fit(X, y)\n",
    "\n",
    "# Plot the decision boundary. For that, we will assign a color to each\n",
    "# point in the mesh [x_min, x_max]x[y_min, y_max].\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "h = .01  # step size in the mesh\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "Z = logreg.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "# Put the result into a color plot\n",
    "Z = Z.reshape(xx.shape)\n",
    "plt.figure(1, figsize=(10, 10))\n",
    "plt.pcolormesh(xx, yy, Z, cmap=plt.cm.RdYlBu, alpha=0.2)\n",
    "\n",
    "# Plot also the training points\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, edgecolors='k', cmap=plt.cm.RdYlBu)\n",
    "plt.xlabel('Sepal length', fontsize=14)\n",
    "plt.ylabel('Sepal width', fontsize=14)\n",
    "\n",
    "plt.xlim(xx.min(), xx.max())\n",
    "plt.ylim(yy.min(), yy.max())\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A real example: Tesla vs SpaceX tweets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "import spacy\n",
    "import nltk\n",
    "import string\n",
    "import sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load the dataset\n",
    "\n",
    "root_folder = \"../data/musk_tweets\"\n",
    "df_elon = pd.read_csv(codecs.open(os.path.join(root_folder,\"df_elon.csv\"), encoding=\"utf8\"), sep=\",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>created_at</th>\n",
       "      <th>text</th>\n",
       "      <th>clean_text</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>849636868052275200</td>\n",
       "      <td>2017-04-05 14:56:29</td>\n",
       "      <td>'And so the robots spared humanity ... https:/...</td>\n",
       "      <td>robots spared humanity</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>848988730585096192</td>\n",
       "      <td>2017-04-03 20:01:01</td>\n",
       "      <td>\"@ForIn2020 @waltmossberg @mims @defcon_5 Exac...</td>\n",
       "      <td>@ForIn2020 @waltmossberg @mims @defcon_5 Exact...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>848943072423497728</td>\n",
       "      <td>2017-04-03 16:59:35</td>\n",
       "      <td>'@waltmossberg @mims @defcon_5 Et tu, Walt?'</td>\n",
       "      <td>@waltmossberg @mims @defcon_5 Walt</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>848935705057280001</td>\n",
       "      <td>2017-04-03 16:30:19</td>\n",
       "      <td>'Stormy weather in Shortville ...'</td>\n",
       "      <td>Stormy weather Shortville</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>848416049573658624</td>\n",
       "      <td>2017-04-02 06:05:23</td>\n",
       "      <td>\"@DaveLeeBBC @verge Coal is dying due to nat g...</td>\n",
       "      <td>@DaveLeeBBC @verge Coal dying fracking It's ba...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   id           created_at  \\\n",
       "0  849636868052275200  2017-04-05 14:56:29   \n",
       "1  848988730585096192  2017-04-03 20:01:01   \n",
       "2  848943072423497728  2017-04-03 16:59:35   \n",
       "3  848935705057280001  2017-04-03 16:30:19   \n",
       "4  848416049573658624  2017-04-02 06:05:23   \n",
       "\n",
       "                                                text  \\\n",
       "0  'And so the robots spared humanity ... https:/...   \n",
       "1  \"@ForIn2020 @waltmossberg @mims @defcon_5 Exac...   \n",
       "2       '@waltmossberg @mims @defcon_5 Et tu, Walt?'   \n",
       "3                 'Stormy weather in Shortville ...'   \n",
       "4  \"@DaveLeeBBC @verge Coal is dying due to nat g...   \n",
       "\n",
       "                                          clean_text  \n",
       "0                             robots spared humanity  \n",
       "1  @ForIn2020 @waltmossberg @mims @defcon_5 Exact...  \n",
       "2                 @waltmossberg @mims @defcon_5 Walt  \n",
       "3                          Stormy weather Shortville  \n",
       "4  @DaveLeeBBC @verge Coal dying fracking It's ba...  "
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_elon.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Filter to just Tesla or SpaceX\n",
    "\n",
    "def classify_t_or_s(tweet):\n",
    "    \n",
    "    if type(tweet) == str and \"@SpaceX\" in tweet:\n",
    "        return 1\n",
    "    elif type(tweet) == str and \"@TeslaMotors\" in tweet:\n",
    "        return 0\n",
    "    return -1\n",
    "\n",
    "def remove_t_or_s(tweet):\n",
    "    \n",
    "    if type(tweet) == str:\n",
    "        removed = tweet.replace(\"@SpaceX\",\"\")\n",
    "        removed = removed.replace(\"@TeslaMotors\",\"\")\n",
    "        return removed\n",
    "    return \"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create classes and remove the discriminant token!\n",
    "df_elon[\"class\"] = df_elon[\"clean_text\"].apply(classify_t_or_s)\n",
    "df_elon[\"clean_text_rm\"] = df_elon[\"clean_text\"].apply(remove_t_or_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>created_at</th>\n",
       "      <th>text</th>\n",
       "      <th>clean_text</th>\n",
       "      <th>class</th>\n",
       "      <th>clean_text_rm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>848239664536223745</td>\n",
       "      <td>2017-04-01 18:24:30</td>\n",
       "      <td>'RT @ProfBrianCox: This is extremely important...</td>\n",
       "      <td>@ProfBrianCox This extremely important from @e...</td>\n",
       "      <td>1</td>\n",
       "      <td>@ProfBrianCox This extremely important from @e...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>847610880506208257</td>\n",
       "      <td>2017-03-31 00:45:56</td>\n",
       "      <td>'RT @SpaceX: More photos from today\\xe2\\x80\\x9...</td>\n",
       "      <td>@SpaceX More photos from today x99s Falcon lau...</td>\n",
       "      <td>1</td>\n",
       "      <td>More photos from today x99s Falcon launch fir...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>847608431582208000</td>\n",
       "      <td>2017-03-31 00:36:12</td>\n",
       "      <td>'@BadAstronomer @SpaceX Thanks Phil!'</td>\n",
       "      <td>@BadAstronomer @SpaceX Thanks Phil</td>\n",
       "      <td>1</td>\n",
       "      <td>@BadAstronomer  Thanks Phil</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>847580067446345728</td>\n",
       "      <td>2017-03-30 22:43:30</td>\n",
       "      <td>'RT @SpaceX: Falcon 9 first stage has landed o...</td>\n",
       "      <td>@SpaceX Falcon first stage landed Course Still...</td>\n",
       "      <td>1</td>\n",
       "      <td>Falcon first stage landed Course Still Love w...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>847561780532523008</td>\n",
       "      <td>2017-03-30 21:30:50</td>\n",
       "      <td>'RT @SpaceX: ~60 minutes until launch window f...</td>\n",
       "      <td>@SpaceX minutes until launch window opens syst...</td>\n",
       "      <td>1</td>\n",
       "      <td>minutes until launch window opens systems wea...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    id           created_at  \\\n",
       "11  848239664536223745  2017-04-01 18:24:30   \n",
       "22  847610880506208257  2017-03-31 00:45:56   \n",
       "23  847608431582208000  2017-03-31 00:36:12   \n",
       "25  847580067446345728  2017-03-30 22:43:30   \n",
       "26  847561780532523008  2017-03-30 21:30:50   \n",
       "\n",
       "                                                 text  \\\n",
       "11  'RT @ProfBrianCox: This is extremely important...   \n",
       "22  'RT @SpaceX: More photos from today\\xe2\\x80\\x9...   \n",
       "23              '@BadAstronomer @SpaceX Thanks Phil!'   \n",
       "25  'RT @SpaceX: Falcon 9 first stage has landed o...   \n",
       "26  'RT @SpaceX: ~60 minutes until launch window f...   \n",
       "\n",
       "                                           clean_text  class  \\\n",
       "11  @ProfBrianCox This extremely important from @e...      1   \n",
       "22  @SpaceX More photos from today x99s Falcon lau...      1   \n",
       "23                 @BadAstronomer @SpaceX Thanks Phil      1   \n",
       "25  @SpaceX Falcon first stage landed Course Still...      1   \n",
       "26  @SpaceX minutes until launch window opens syst...      1   \n",
       "\n",
       "                                        clean_text_rm  \n",
       "11  @ProfBrianCox This extremely important from @e...  \n",
       "22   More photos from today x99s Falcon launch fir...  \n",
       "23                        @BadAstronomer  Thanks Phil  \n",
       "25   Falcon first stage landed Course Still Love w...  \n",
       "26   minutes until launch window opens systems wea...  "
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_elon[df_elon[\"class\"] == 1].head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(316, 6)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_reduced = df_elon[df_elon[\"class\"] != -1]\n",
    "df_reduced.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(316, 1330)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's create the TF-IDF representation of the dataset\n",
    "\n",
    "from nltk.tokenize import TweetTokenizer\n",
    "tknzr = TweetTokenizer(preserve_case=False, reduce_len=False, strip_handles=False)\n",
    "\n",
    "from sklearn.feature_extraction.text import CountVectorizer\n",
    "count_vect = CountVectorizer(tokenizer=tknzr.tokenize)\n",
    "X = count_vect.fit_transform(df_reduced.clean_text_rm)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = df_reduced[\"class\"].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='warn', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg = LogisticRegression(solver='lbfgs')\n",
    "\n",
    "# Create an instance of Logistic Regression Classifier and fit the data.\n",
    "logreg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "[0.72029129 0.27970871]\n"
     ]
    }
   ],
   "source": [
    "# Try it out\n",
    "\n",
    "test_tweet1 = \"Let's all go to Mars and colonize!\"\n",
    "test_tweet2 = \"Let's all go on with an electric car with auto pilot\"\n",
    "x = count_vect.transform([test_tweet2])\n",
    "print(logreg.predict(x)[0])\n",
    "print(logreg.predict_proba(x)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<1x1330 sparse matrix of type '<class 'numpy.int64'>'\n",
       "\twith 1 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*But, does it actually work?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exploratory vs confirmatory modelling\n",
    "\n",
    "\"Traditionally, the focus of modelling is on *inference, or for confirming that an hypothesis is \"true\"*. Doing this correctly is not complicated, but it is hard. There is a pair of ideas that you must understand in order to do inference correctly:\n",
    "\n",
    "* Each observation can either be used for exploration or confirmation, not both.\n",
    "\n",
    "* You can use an observation as many times as you like for exploration, but you can only use it once for confirmation. As soon as you use an observation twice, you’ve switched from confirmation to exploration.\n",
    "\n",
    "This is necessary because to confirm a hypothesis you must use data independent of the data that you used to generate the hypothesis. Otherwise you will be over optimistic. There is absolutely nothing wrong with exploration, but you should never sell an exploratory analysis as a confirmatory analysis because it is fundamentally misleading.\n",
    "\n",
    "If you are serious about doing an confirmatory analysis, one approach is to split your data into three pieces before you begin the analysis:\n",
    "\n",
    "* 60% of your data goes into a **training** (or exploration) set. You’re allowed to do anything you like with this data: visualise it and fit tons of models to it.\n",
    "\n",
    "* 20% goes into a **validation** set. You can use this data to compare models or visualisations by hand, but you’re not allowed to use it as part of an automated process.\n",
    "\n",
    "* 20% is held back for a **test** set. You can only use this data ONCE, to test your final model.\n",
    "\n",
    "This partitioning allows you to explore the training data, occasionally generating candidate hypotheses that you check with the query set. When you are confident you have the right model, you can check it once with the test data.\"\n",
    "\n",
    "https://r4ds.had.co.nz/model-intro.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=1)\n",
    "X_train, X_val, y_train, y_val = train_test_split(X_train, y_train, test_size=0.5, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7789473684210526\n",
      "74\n"
     ]
    }
   ],
   "source": [
    "logreg.fit(X_train, y_train)\n",
    "y_hat_test = logreg.predict(X_test)\n",
    "\n",
    "# evaluate using accuracy: proportion of correctly predicted over total\n",
    "from sklearn.metrics import accuracy_score\n",
    "print(accuracy_score(y_test, y_hat_test))\n",
    "print(accuracy_score(y_test, y_hat_test, normalize=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are doing well already! Try to play with the model or with the pre-processing and test against the test set. When you are happy, do a final evaluation against the validation set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Questions\n",
    "\n",
    "* Read about precision and recall: https://en.wikipedia.org/wiki/Precision_and_recall. Add them to the evaluation above. Hint: see the `precision_score` and `recall_score` here: https://scikit-learn.org/stable/modules/model_evaluation.html.\n",
    "* Build a multiclass logistic classifier for the BL book genre (perhaps during the afternoon session)."
   ]
  }
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